Subgroups — C₄₁×#24778 #23800979

Order 10496.

1066 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2414	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2065	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2034	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1875	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₁	C₂²	1	2	yes	—
16	C₂×#121×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₁	C₂²	1	2	yes	—
19	C₄₁×#466	—	2	4	no	—
20	C₄₁×#466	—	2	4	no	—
21	C₈×D₄×C₄₁	—	2	4	no	—
22	C₄₁×#427	—	2	4	no	—
23	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#106×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₁	C₂²	1	2	yes	—
29	C₂×#102×C₄₁	C₂²	1	2	yes	—
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#394	—	2	2	no	—
35	C₄₁×#392	—	2	2	no	—
36	C₄₁×#390	—	2	2	no	—
37	C₄₁×#390	C₂²	1	2	yes	—
38	C₄₁×#389	C₂²	1	2	yes	—
39	C₄₁×#388	—	2	2	no	—
40	C₄₁×#380	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₁	—	2	2	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₄₁	—	2	2	no	—
50	C₂×D₈×C₄₁	—	2	2	no	—
51	C₂×D₈×C₄₁	—	2	2	no	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	—	2	2	no	—
54	C₂²×C₈×C₄₁	—	2	2	no	—
55	C₂²×C₈×C₄₁	—	2	2	no	—
56	C₂²×C₈×C₄₁	—	2	2	no	—
57	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
58	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
62	#121×C₄₁	—	2	4	no	—
63	#121×C₄₁	—	2	4	no	—
64	#121×C₄₁	—	2	4	no	—
65	#121×C₄₁	—	4	2	no	—
66	C₄×D₄×C₄₁	—	2	2	no	—
67	C₄×D₄×C₄₁	—	2	2	no	—
68	#117×C₄₁	—	2	4	no	—
69	#117×C₄₁	—	4	2	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₁	—	2	2	no	—
84	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
85	#107×C₄₁	—	2	2	no	—
86	#107×C₄₁	—	2	2	no	—
87	#107×C₄₁	D₄	1	4	yes	complemented
88	#106×C₄₁	—	2	4	no	—
89	C₄⋊C₈×C₄₁	—	2	2	no	—
90	#102×C₄₁	—	2	4	no	—
91	#102×C₄₁	—	2	4	no	—
92	#102×C₄₁	—	4	2	no	—
93	C₂²⋊C₈×C₄₁	—	2	2	no	—
94	C₂²⋊C₈×C₄₁	—	2	2	no	—
95	C₄×C₈×C₄₁	—	2	2	no	—
96	#95×C₄₁	—	2	2	no	—
97	#95×C₄₁	—	2	2	no	—
98	C₂⁴×C₄₁	—	2	2	no	—
99	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	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	—	2	2	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	4	4	no	—
111	C₂×D₄×C₄₁	—	4	4	no	—
112	C₂×D₄×C₄₁	—	4	4	no	—
113	C₂×D₄×C₄₁	—	8	2	no	—
114	C₂×D₄×C₄₁	—	8	2	no	—
115	C₂×D₄×C₄₁	—	8	2	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	—	2	1	no	—
123	C₂²×C₄×C₄₁	—	2	1	no	—
124	C₂²×C₄×C₄₁	—	2	1	no	—
125	C₂²×C₄×C₄₁	—	2	1	no	—
126	C₂²×C₄×C₄₁	—	2	1	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	#41	1	2	yes	—
135	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
136	D₈×C₄₁	—	4	4	no	—
137	C₂×C₈×C₄₁	—	2	1	no	—
138	C₂×C₈×C₄₁	—	2	1	no	—
139	C₂×C₈×C₄₁	—	2	8	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	1	no	—
145	C₂×C₈×C₄₁	—	2	1	no	—
146	C₂×C₈×C₄₁	—	4	4	no	—
147	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₄₁	#41	1	2	yes	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	2	no	—
153	C₄⋊C₄×C₄₁	—	2	2	no	—
154	C₄⋊C₄×C₄₁	—	2	2	no	—
155	C₄⋊C₄×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	2	no	—
157	C₄⋊C₄×C₄₁	—	8	2	no	—
158	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
159	C₂²⋊C₄×C₄₁	—	2	2	no	—
160	C₂²⋊C₄×C₄₁	—	2	2	no	—
161	C₂²⋊C₄×C₄₁	—	4	4	no	—
162	C₂²⋊C₄×C₄₁	—	4	4	no	—
163	C₂²⋊C₄×C₄₁	—	4	4	no	—
164	C₂²⋊C₄×C₄₁	—	4	4	no	—
165	C₂²⋊C₄×C₄₁	—	8	2	no	—
166	C₂²⋊C₄×C₄₁	—	8	2	no	—
167	C₄²×C₄₁	—	2	1	no	—
168	C₄²×C₄₁	—	2	1	no	—
169	C₄²×C₄₁	—	4	4	no	—
170	C₂³×C₄₁	—	2	1	no	—
171	C₂³×C₄₁	—	2	1	no	—
172	C₂³×C₄₁	—	2	1	no	—
173	C₂³×C₄₁	—	2	1	no	—
174	C₂³×C₄₁	—	2	1	no	—
175	C₂³×C₄₁	—	2	1	no	—
176	C₂³×C₄₁	—	2	1	no	—
177	C₂³×C₄₁	—	2	1	no	—
178	C₂³×C₄₁	—	2	1	no	—
179	C₂³×C₄₁	—	2	1	no	—
180	C₂³×C₄₁	—	2	1	no	—
181	C₂³×C₄₁	—	2	1	no	—
182	C₂³×C₄₁	—	4	2	no	—
183	C₂³×C₄₁	—	4	2	no	—
184	C₂³×C₄₁	—	4	2	no	—
185	C₂³×C₄₁	—	4	2	no	—
186	C₂³×C₄₁	—	4	2	no	—
187	C₂³×C₄₁	—	4	2	no	—
188	C₂³×C₄₁	—	4	2	no	—
189	C₂³×C₄₁	#121	1	2	yes	—
190	C₂³×C₄₁	#135	1	2	yes	—
191	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
192	D₄×C₄₁	—	2	8	no	—
193	D₄×C₄₁	—	4	2	no	—
194	D₄×C₄₁	—	4	2	no	—
195	D₄×C₄₁	—	4	2	no	—
196	D₄×C₄₁	—	4	2	no	—
197	D₄×C₄₁	—	8	8	no	—
198	D₄×C₄₁	—	8	8	no	—
199	C₂×C₄×C₄₁	—	2	1	no	—
200	C₂×C₄×C₄₁	—	2	1	no	—
201	C₂×C₄×C₄₁	—	2	1	no	—
202	C₂×C₄×C₄₁	—	2	1	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	2	no	—
207	C₂×C₄×C₄₁	—	2	1	no	—
208	C₂×C₄×C₄₁	—	2	1	no	—
209	C₂×C₄×C₄₁	—	2	4	no	—
210	C₂×C₄×C₄₁	—	2	1	no	—
211	C₂×C₄×C₄₁	—	2	1	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	1	no	—
214	C₂×C₄×C₄₁	—	4	2	no	—
215	C₂×C₄×C₄₁	—	4	2	no	—
216	C₂×C₄×C₄₁	—	4	1	no	—
217	C₂×C₄×C₄₁	—	4	1	no	—
218	C₂×C₄×C₄₁	—	4	1	no	—
219	C₂×C₄×C₄₁	—	4	1	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	2	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	#121	1	2	yes	—
227	C₂×C₄×C₄₁	#135	1	2	yes	—
228	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
234	C₈×C₄₁	—	2	2	no	—
235	C₈×C₄₁	—	4	1	no	—
236	C₈×C₄₁	—	4	1	no	—
237	C₈×C₄₁	#121	1	4	yes	—
238	#24778	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₄₁	—	2	2	no	—
240	C₂²×C₄₁	—	2	2	no	—
241	C₂²×C₄₁	—	2	2	no	—
242	C₂²×C₄₁	—	2	2	no	—
243	C₂²×C₄₁	—	2	2	no	—
244	C₂²×C₄₁	—	2	2	no	—
245	C₂²×C₄₁	—	4	1	no	—
246	C₂²×C₄₁	—	4	1	no	—
247	C₂²×C₄₁	—	4	1	no	—
248	C₂²×C₄₁	—	4	1	no	—
249	C₂²×C₄₁	—	4	1	no	—
250	C₂²×C₄₁	—	4	1	no	—
251	C₂²×C₄₁	—	4	1	no	—
252	C₂²×C₄₁	—	4	1	no	—
253	C₂²×C₄₁	—	8	2	no	—
254	C₂²×C₄₁	—	8	2	no	—
255	C₂²×C₄₁	—	8	2	no	—
256	C₂²×C₄₁	—	8	2	no	—
257	C₂²×C₄₁	—	8	2	no	—
258	C₂²×C₄₁	—	8	2	no	—
259	C₂²×C₄₁	—	8	2	no	—
260	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
261	C₂²×C₄₁	D₄²	1	1	yes	characteristic
262	C₂²×C₄₁	#547	1	1	yes	characteristic
263	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
264	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
265	C₂²×C₄₁	#576	1	1	yes	characteristic
266	C₂²×C₄₁	#576	1	1	yes	characteristic
267	C₄×C₄₁	—	2	2	no	—
268	C₄×C₄₁	—	2	2	no	—
269	C₄×C₄₁	—	4	1	no	—
270	C₄×C₄₁	—	4	4	no	—
271	C₄×C₄₁	—	4	1	no	—
272	C₄×C₄₁	—	8	2	no	—
273	C₄×C₄₁	—	8	2	no	—
274	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
275	C₄×C₄₁	#537	1	1	yes	characteristic
276	C₄×C₄₁	#548	1	1	yes	characteristic
277	C₄×C₄₁	#553	1	1	yes	characteristic
278	C₂×#466	C₂×C₄₁	1	1	yes	characteristic, complemented
279	C₂×#466	C₂×C₄₁	1	1	yes	characteristic, complemented
280	C₂×C₈×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
281	C₂×#427	C₂×C₄₁	1	1	yes	characteristic, complemented
282	#2414	C₂×C₄₁	1	2	yes	complemented
283	#2065	C₂×C₄₁	1	2	yes	complemented
284	#2034	C₂×C₄₁	1	2	yes	complemented
285	#1970	C₂×C₄₁	1	1	yes	characteristic, complemented
286	#1942	C₂×C₄₁	1	1	yes	characteristic, complemented
287	#1875	C₂×C₄₁	1	2	yes	complemented
288	#1808	C₂×C₄₁	1	1	yes	characteristic, complemented
289	C₂×C₄₁	—	4	2	no	—
290	C₂×C₄₁	—	4	2	no	—
291	C₂×C₄₁	—	16	2	no	—
292	C₂×C₄₁	#2416	1	1	yes	characteristic
293	C₂×C₄₁	#3050	1	1	yes	characteristic
294	C₂×C₄₁	#3058	1	1	yes	characteristic
295	C₂×C₄₁	#3280	1	1	yes	characteristic
296	C₂×C₄₁	#3287	1	1	yes	characteristic
297	C₂×C₄₁	#3339	1	1	yes	characteristic
298	C₂×C₄₁	#3341	1	1	yes	characteristic
299	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
300	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
301	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
302	C₂×#121	C₂²×C₄₁	1	2	yes	—
303	C₂×#121	C₂²×C₄₁	1	2	yes	—
304	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
305	C₂×#117	C₂²×C₄₁	1	2	yes	—
306	#466	—	2	4	no	—
307	#466	—	2	4	no	—
308	C₈×D₄	—	2	4	no	—
309	#427	—	2	4	no	—
310	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
311	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
312	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
313	C₂×#106	C₂²×C₄₁	1	2	yes	—
314	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
315	C₂×#102	C₂²×C₄₁	1	2	yes	—
316	C₂×#102	C₂²×C₄₁	1	2	yes	—
317	C₂×#102	C₂²×C₄₁	1	2	yes	—
318	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
320	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
321	#394	—	2	2	no	—
322	#392	—	2	2	no	—
323	#390	—	2	2	no	—
324	#390	C₂²×C₄₁	1	2	yes	—
325	#389	C₂²×C₄₁	1	2	yes	—
326	#388	—	2	2	no	—
327	#380	C₂²×C₄₁	1	2	yes	—
328	#340	C₂²×C₄₁	1	2	yes	—
329	#340	C₂²×C₄₁	1	2	yes	—
330	C₄₁	#24778	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
334	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
335	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
337	C₂×D₈	—	2	2	no	—
338	C₂×D₈	—	2	2	no	—
339	C₂×D₈	—	2	2	no	—
340	C₂²×C₈	—	2	2	no	—
341	C₂²×C₈	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
346	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
350	#121	—	2	4	no	—
351	#121	—	2	4	no	—
352	#121	—	2	4	no	—
353	#121	—	4	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	#117	—	2	4	no	—
357	#117	—	4	2	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
371	C₂×C₄²	—	2	2	no	—
372	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
373	#107	—	2	2	no	—
374	#107	—	2	2	no	—
375	#107	D₄×C₄₁	1	4	yes	complemented
376	#106	—	2	4	no	—
377	C₄⋊C₈	—	2	2	no	—
378	#102	—	2	4	no	—
379	#102	—	2	4	no	—
380	#102	—	4	2	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	C₂²⋊C₈	—	2	2	no	—
383	C₄×C₈	—	2	2	no	—
384	#95	—	2	2	no	—
385	#95	—	2	2	no	—
386	C₂⁴	—	2	2	no	—
387	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
388	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	8	2	no	—
402	C₂×D₄	—	8	2	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
421	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
422	C₂²×C₄	#41×C₄₁	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
424	D₈	—	4	4	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	8	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	4	4	no	—
435	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
436	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
437	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
438	C₂×C₈	#41×C₄₁	1	2	yes	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	8	2	no	—
446	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	4	4	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	4	no	—
453	C₂²⋊C₄	—	8	2	no	—
454	C₂²⋊C₄	—	8	2	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	4	4	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	#121×C₄₁	1	2	yes	—
478	C₂³	#135×C₄₁	1	2	yes	—
479	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
480	D₄	—	2	8	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	8	8	no	—
486	D₄	—	8	8	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	#121×C₄₁	1	2	yes	—
515	C₂×C₄	#135×C₄₁	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
519	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
520	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
521	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
522	C₈	—	2	2	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	#121×C₄₁	1	4	yes	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
548	C₂²	D₄²×C₄₁	1	1	yes	characteristic
549	C₂²	C₄₁×#547	1	1	yes	characteristic
550	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
551	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
552	C₂²	C₄₁×#576	1	1	yes	characteristic
553	C₂²	C₄₁×#576	1	1	yes	characteristic
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	4	no	—
559	C₄	—	8	2	no	—
560	C₄	—	8	2	no	—
561	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
562	C₄	C₄₁×#537	1	1	yes	characteristic
563	C₄	C₄₁×#548	1	1	yes	characteristic
564	C₄	C₄₁×#553	1	1	yes	characteristic
565	C₂	—	4	2	no	—
566	C₂	—	4	2	no	—
567	C₂	—	16	2	no	—
568	C₂	C₄₁×#2416	1	1	yes	characteristic
569	C₂	C₄₁×#3050	1	1	yes	characteristic
570	C₂	C₄₁×#3058	1	1	yes	characteristic
571	C₂	C₄₁×#3280	1	1	yes	characteristic
572	C₂	C₄₁×#3287	1	1	yes	characteristic
573	C₂	C₄₁×#3339	1	1	yes	characteristic
574	C₂	C₄₁×#3341	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#466	C₂	semidirect
2. C₂×C₄₁×#466	C₂	semidirect
3. C₂×C₈×D₄×C₄₁	C₂	semidirect
4. C₂×C₄₁×#427	C₂	semidirect
5. C₄₁×#2414	C₂	semidirect
6. C₄₁×#2065	C₂	semidirect
7. C₄₁×#2034	C₂	semidirect
8. C₄₁×#1970	C₂	semidirect
9. C₄₁×#1942	C₂	semidirect
10. C₄₁×#1875	C₂	semidirect
11. C₄₁×#1808	C₂	semidirect
57. C₂²×C₈×C₄₁	D₄	semidirect
87. #107×C₄₁	D₄	semidirect
238. #24778	C₄₁	direct (N × H)
278. C₂×#466	C₂×C₄₁	semidirect
279. C₂×#466	C₂×C₄₁	semidirect
280. C₂×C₈×D₄	C₂×C₄₁	semidirect
281. C₂×#427	C₂×C₄₁	semidirect
282. #2414	C₂×C₄₁	semidirect
283. #2065	C₂×C₄₁	semidirect
284. #2034	C₂×C₄₁	semidirect
285. #1970	C₂×C₄₁	semidirect
286. #1942	C₂×C₄₁	semidirect
287. #1875	C₂×C₄₁	semidirect
288. #1808	C₂×C₄₁	semidirect
330. C₄₁	#24778	direct (N × H)
345. C₂²×C₈	D₄×C₄₁	semidirect
375. #107	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×#466	2
C₂×C₈×D₄×C₄₁	2
C₂×C₄₁×#427	2
C₄₁×#2414	2
C₄₁×#2065	2
C₄₁×#2034	2
C₄₁×#1970	2
C₄₁×#1942	2
C₄₁×#1875	2
C₄₁×#1808	2
#24778	41

Subgroups — C41×#24778 #23800979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24778 #23800979