Subgroups — C₄₁×#25414 #23801615

Order 10496.

1238 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2428	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2041	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1999	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×#1879	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₁	C₂²	1	2	yes	—
17	C₂×#121×C₄₁	—	2	2	no	—
18	C₂×#121×C₄₁	C₂²	1	2	yes	—
19	C₂×#121×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#493	—	2	4	no	—
22	C₄₁×#466	—	2	4	no	—
23	C₄₁×#466	—	2	4	no	—
24	C₄×D₈×C₄₁	—	2	4	no	—
25	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
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×C₄×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	C₂²	1	2	yes	—
37	C₄₁×#389	C₂²	1	2	yes	—
38	C₄₁×#386	—	2	2	no	—
39	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	1	yes	characteristic
42	C₄₁×#336	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₄₁	—	2	2	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	2	no	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₁	—	2	2	no	—
50	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
51	C₂×D₈×C₄₁	—	2	4	no	—
52	C₂×D₈×C₄₁	—	2	2	no	—
53	C₂×D₈×C₄₁	—	2	2	no	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	—	2	2	no	—
56	C₂×D₈×C₄₁	—	2	4	no	—
57	C₂×D₈×C₄₁	—	2	2	no	—
58	C₂×D₈×C₄₁	—	4	2	no	—
59	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
60	C₂²×C₈×C₄₁	—	2	2	no	—
61	C₂²×C₈×C₄₁	—	2	2	no	—
62	C₂²×C₈×C₄₁	—	2	2	no	—
63	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	#127×C₄₁	—	2	4	no	—
68	#127×C₄₁	—	4	2	no	—
69	#121×C₄₁	—	2	4	no	—
70	#121×C₄₁	—	2	4	no	—
71	#121×C₄₁	—	4	2	no	—
72	#121×C₄₁	—	4	2	no	—
73	#121×C₄₁	—	4	8	no	—
74	C₄×D₄×C₄₁	—	2	4	no	—
75	C₄×D₄×C₄₁	—	4	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
88	#107×C₄₁	—	2	2	no	—
89	#107×C₄₁	D₄	1	4	yes	complemented
90	#102×C₄₁	—	2	4	no	—
91	#102×C₄₁	—	2	4	no	—
92	#102×C₄₁	—	2	4	no	—
93	#102×C₄₁	—	4	2	no	—
94	C₂²⋊C₈×C₄₁	—	2	2	no	—
95	C₄×C₈×C₄₁	—	2	2	no	—
96	C₄×C₈×C₄₁	—	2	2	no	—
97	#95×C₄₁	—	2	2	no	—
98	#95×C₄₁	D₄	1	1	yes	characteristic
99	#95×C₄₁	D₄	1	1	yes	characteristic
100	C₂⁴×C₄₁	—	2	2	no	—
101	C₂⁴×C₄₁	—	2	2	no	—
102	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
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	—	4	4	no	—
115	C₂×D₄×C₄₁	—	4	4	no	—
116	C₂×D₄×C₄₁	—	4	4	no	—
117	C₂×D₄×C₄₁	—	4	4	no	—
118	C₂×D₄×C₄₁	—	4	4	no	—
119	C₂×D₄×C₄₁	—	4	4	no	—
120	C₂×D₄×C₄₁	—	4	4	no	—
121	C₂×D₄×C₄₁	—	4	4	no	—
122	C₂×D₄×C₄₁	—	8	2	no	—
123	C₂×D₄×C₄₁	—	8	2	no	—
124	C₂×D₄×C₄₁	—	8	2	no	—
125	C₂×D₄×C₄₁	—	8	2	no	—
126	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	1	no	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	—	2	1	no	—
132	C₂²×C₄×C₄₁	—	2	1	no	—
133	C₂²×C₄×C₄₁	—	2	1	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	4	4	no	—
136	C₂²×C₄×C₄₁	—	4	4	no	—
137	C₂²×C₄×C₄₁	—	8	2	no	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
144	D₈×C₄₁	—	2	8	no	—
145	D₈×C₄₁	—	4	8	no	—
146	D₈×C₄₁	—	4	4	no	—
147	C₂×C₈×C₄₁	—	2	1	no	—
148	C₂×C₈×C₄₁	—	2	1	no	—
149	C₂×C₈×C₄₁	—	2	1	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	1	no	—
155	C₂×C₈×C₄₁	—	4	4	no	—
156	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₄₁	#41	1	2	yes	—
159	C₂×C₈×C₄₁	#41	1	2	yes	—
160	C₄⋊C₄×C₄₁	—	2	2	no	—
161	C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₄⋊C₄×C₄₁	—	2	2	no	—
163	C₄⋊C₄×C₄₁	—	4	4	no	—
164	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
165	C₂²⋊C₄×C₄₁	—	2	2	no	—
166	C₂²⋊C₄×C₄₁	—	4	4	no	—
167	C₂²⋊C₄×C₄₁	—	4	4	no	—
168	C₂²⋊C₄×C₄₁	—	4	4	no	—
169	C₂²⋊C₄×C₄₁	—	4	4	no	—
170	C₂²⋊C₄×C₄₁	—	8	2	no	—
171	C₂²⋊C₄×C₄₁	D₈	1	4	yes	complemented
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	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	—	2	4	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	—	4	2	no	—
190	C₂³×C₄₁	—	4	2	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	2	no	—
193	C₂³×C₄₁	—	4	2	no	—
194	C₂³×C₄₁	—	4	2	no	—
195	C₂³×C₄₁	—	4	2	no	—
196	C₂³×C₄₁	C₂×D₈	1	2	yes	—
197	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
198	D₄×C₄₁	—	2	4	no	—
199	D₄×C₄₁	—	2	4	no	—
200	D₄×C₄₁	—	4	2	no	—
201	D₄×C₄₁	—	4	2	no	—
202	D₄×C₄₁	—	4	2	no	—
203	D₄×C₄₁	—	4	2	no	—
204	D₄×C₄₁	—	4	2	no	—
205	D₄×C₄₁	—	4	2	no	—
206	D₄×C₄₁	—	8	8	no	—
207	D₄×C₄₁	—	8	8	no	—
208	D₄×C₄₁	—	8	8	no	—
209	D₄×C₄₁	—	8	8	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	—	2	1	no	—
215	C₂×C₄×C₄₁	—	2	1	no	—
216	C₂×C₄×C₄₁	—	2	1	no	—
217	C₂×C₄×C₄₁	—	2	1	no	—
218	C₂×C₄×C₄₁	—	2	1	no	—
219	C₂×C₄×C₄₁	—	2	1	no	—
220	C₂×C₄×C₄₁	—	2	4	no	—
221	C₂×C₄×C₄₁	—	2	1	no	—
222	C₂×C₄×C₄₁	—	2	1	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	1	no	—
226	C₂×C₄×C₄₁	—	4	1	no	—
227	C₂×C₄×C₄₁	—	4	1	no	—
228	C₂×C₄×C₄₁	—	4	1	no	—
229	C₂×C₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	4	2	no	—
232	C₂×C₄×C₄₁	—	8	8	no	—
233	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
234	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
235	C₂×C₄×C₄₁	#135	1	2	yes	—
236	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
242	C₈×C₄₁	—	2	2	no	—
243	C₈×C₄₁	—	4	1	no	—
244	C₈×C₄₁	—	4	1	no	—
245	C₈×C₄₁	#121	1	4	yes	complemented
246	#25414	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₄₁	—	2	2	no	—
248	C₂²×C₄₁	—	2	2	no	—
249	C₂²×C₄₁	—	2	2	no	—
250	C₂²×C₄₁	—	4	1	no	—
251	C₂²×C₄₁	—	4	1	no	—
252	C₂²×C₄₁	—	4	1	no	—
253	C₂²×C₄₁	—	4	1	no	—
254	C₂²×C₄₁	—	4	4	no	—
255	C₂²×C₄₁	—	4	4	no	—
256	C₂²×C₄₁	—	4	4	no	—
257	C₂²×C₄₁	—	8	2	no	—
258	C₂²×C₄₁	—	8	2	no	—
259	C₂²×C₄₁	—	8	2	no	—
260	C₂²×C₄₁	—	8	2	no	—
261	C₂²×C₄₁	—	8	2	no	—
262	C₂²×C₄₁	—	8	2	no	—
263	C₂²×C₄₁	—	8	2	no	—
264	C₂²×C₄₁	—	8	2	no	—
265	C₂²×C₄₁	—	8	2	no	—
266	C₂²×C₄₁	—	8	2	no	—
267	C₂²×C₄₁	—	8	2	no	—
268	C₂²×C₄₁	#532	1	1	yes	characteristic
269	C₂²×C₄₁	D₄²	1	1	yes	characteristic
270	C₂²×C₄₁	D₄²	1	1	yes	characteristic
271	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
272	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
273	C₂²×C₄₁	#576	1	1	yes	characteristic
274	C₂²×C₄₁	#576	1	1	yes	characteristic
275	C₄×C₄₁	—	2	2	no	—
276	C₄×C₄₁	—	2	2	no	—
277	C₄×C₄₁	—	2	2	no	—
278	C₄×C₄₁	—	4	1	no	—
279	C₄×C₄₁	—	4	4	no	—
280	C₄×C₄₁	—	4	1	no	—
281	C₄×C₄₁	—	8	2	no	—
282	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
283	C₄×C₄₁	#540	1	1	yes	characteristic
284	C₄×C₄₁	#546	1	1	yes	characteristic
285	C₄×C₄₁	#550	1	1	yes	characteristic
286	C₂×#493	C₂×C₄₁	1	1	yes	characteristic, complemented
287	C₂×#466	C₂×C₄₁	1	1	yes	characteristic, complemented
288	C₂×#466	C₂×C₄₁	1	1	yes	characteristic, complemented
289	C₂×C₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
290	#2428	C₂×C₄₁	1	2	yes	complemented
291	#2041	C₂×C₄₁	1	2	yes	complemented
292	#1999	C₂×C₄₁	1	2	yes	complemented
293	#1970	C₂×C₄₁	1	1	yes	characteristic, complemented
294	#1942	C₂×C₄₁	1	1	yes	characteristic, complemented
295	#1879	C₂×C₄₁	1	2	yes	complemented
296	C₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
297	C₂×C₄₁	—	4	2	no	—
298	C₂×C₄₁	—	8	4	no	—
299	C₂×C₄₁	—	16	2	no	—
300	C₂×C₄₁	#2428	1	1	yes	characteristic
301	C₂×C₄₁	#3169	1	1	yes	characteristic
302	C₂×C₄₁	#3176	1	1	yes	characteristic
303	C₂×C₄₁	D₄×D₈	1	1	yes	characteristic
304	C₂×C₄₁	D₄×D₈	1	1	yes	characteristic
305	C₂×C₄₁	#3280	1	1	yes	characteristic
306	C₂×C₄₁	#3287	1	1	yes	characteristic
307	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
308	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
309	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
311	C₂×#127	C₂²×C₄₁	1	2	yes	—
312	C₂×#121	—	2	2	no	—
313	C₂×#121	C₂²×C₄₁	1	2	yes	—
314	C₂×#121	C₂²×C₄₁	1	2	yes	—
315	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
316	#493	—	2	4	no	—
317	#466	—	2	4	no	—
318	#466	—	2	4	no	—
319	C₄×D₈	—	2	4	no	—
320	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
321	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
322	C₂×#102	C₂²×C₄₁	1	2	yes	—
323	C₂×#102	C₂²×C₄₁	1	2	yes	—
324	C₂×#102	C₂²×C₄₁	1	2	yes	—
325	C₂×#102	C₂²×C₄₁	1	2	yes	—
326	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
327	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
328	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
329	#394	—	2	2	no	—
330	#392	—	2	2	no	—
331	#390	C₂²×C₄₁	1	2	yes	—
332	#389	C₂²×C₄₁	1	2	yes	—
333	#386	—	2	2	no	—
334	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
335	#340	C₂²×C₄₁	1	2	yes	—
336	#336	C₂²×C₄₁	1	1	yes	characteristic
337	#336	C₂²×C₄₁	1	1	yes	characteristic
338	C₄₁	#25414	1	1	yes	characteristic, direct product factor, Sylow
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
344	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
347	C₂×D₈	—	2	4	no	—
348	C₂×D₈	—	2	2	no	—
349	C₂×D₈	—	2	2	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×D₈	—	2	2	no	—
352	C₂×D₈	—	2	4	no	—
353	C₂×D₈	—	2	2	no	—
354	C₂×D₈	—	4	2	no	—
355	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
356	C₂²×C₈	—	2	2	no	—
357	C₂²×C₈	—	2	2	no	—
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
363	#127	—	2	4	no	—
364	#127	—	4	2	no	—
365	#121	—	2	4	no	—
366	#121	—	2	4	no	—
367	#121	—	4	2	no	—
368	#121	—	4	2	no	—
369	#121	—	4	8	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	4	2	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
374	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
384	#107	—	2	2	no	—
385	#107	D₄×C₄₁	1	4	yes	complemented
386	#102	—	2	4	no	—
387	#102	—	2	4	no	—
388	#102	—	2	4	no	—
389	#102	—	4	2	no	—
390	C₂²⋊C₈	—	2	2	no	—
391	C₄×C₈	—	2	2	no	—
392	C₄×C₈	—	2	2	no	—
393	#95	—	2	2	no	—
394	#95	D₄×C₄₁	1	1	yes	characteristic
395	#95	D₄×C₄₁	1	1	yes	characteristic
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	8	2	no	—
419	C₂×D₄	—	8	2	no	—
420	C₂×D₄	—	8	2	no	—
421	C₂×D₄	—	8	2	no	—
422	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	8	2	no	—
434	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
440	D₈	—	2	8	no	—
441	D₈	—	4	8	no	—
442	D₈	—	4	4	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	4	4	no	—
452	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
453	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
454	C₂×C₈	#41×C₄₁	1	2	yes	—
455	C₂×C₈	#41×C₄₁	1	2	yes	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	8	2	no	—
467	C₂²⋊C₄	D₈×C₄₁	1	4	yes	complemented
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	C₂×D₈×C₄₁	1	2	yes	—
493	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	8	no	—
503	D₄	—	8	8	no	—
504	D₄	—	8	8	no	—
505	D₄	—	8	8	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	8	8	no	—
529	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
530	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
531	C₂×C₄	#135×C₄₁	1	2	yes	—
532	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
534	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
536	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
537	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	#121×C₄₁	1	4	yes	complemented
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	8	2	no	—
553	C₂²	—	8	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	2	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	C₄₁×#532	1	1	yes	characteristic
564	C₂²	D₄²×C₄₁	1	1	yes	characteristic
565	C₂²	D₄²×C₄₁	1	1	yes	characteristic
566	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
567	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
568	C₂²	C₄₁×#576	1	1	yes	characteristic
569	C₂²	C₄₁×#576	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	1	no	—
576	C₄	—	8	2	no	—
577	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
578	C₄	C₄₁×#540	1	1	yes	characteristic
579	C₄	C₄₁×#546	1	1	yes	characteristic
580	C₄	C₄₁×#550	1	1	yes	characteristic
581	C₂	—	4	2	no	—
582	C₂	—	8	4	no	—
583	C₂	—	16	2	no	—
584	C₂	C₄₁×#2428	1	1	yes	characteristic
585	C₂	C₄₁×#3169	1	1	yes	characteristic
586	C₂	C₄₁×#3176	1	1	yes	characteristic
587	C₂	D₄×D₈×C₄₁	1	1	yes	characteristic
588	C₂	D₄×D₈×C₄₁	1	1	yes	characteristic
589	C₂	C₄₁×#3280	1	1	yes	characteristic
590	C₂	C₄₁×#3287	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 ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#493	C₂	semidirect
2. C₂×C₄₁×#466	C₂	semidirect
3. C₂×C₄₁×#466	C₂	semidirect
4. C₂×C₄×D₈×C₄₁	C₂	semidirect
5. C₄₁×#2428	C₂	semidirect
6. C₄₁×#2041	C₂	semidirect
7. C₄₁×#1999	C₂	semidirect
8. C₄₁×#1970	C₂	semidirect
9. C₄₁×#1942	C₂	semidirect
10. C₄₁×#1879	C₂	semidirect
11. C₈×C₂²⋊C₄×C₄₁	C₂	semidirect
59. C₂×D₈×C₄₁	D₄	semidirect
89. #107×C₄₁	D₄	semidirect
171. C₂²⋊C₄×C₄₁	D₈	semidirect
245. C₈×C₄₁	#121	semidirect
246. #25414	C₄₁	direct (N × H)
286. C₂×#493	C₂×C₄₁	semidirect
287. C₂×#466	C₂×C₄₁	semidirect
288. C₂×#466	C₂×C₄₁	semidirect
289. C₂×C₄×D₈	C₂×C₄₁	semidirect
290. #2428	C₂×C₄₁	semidirect
291. #2041	C₂×C₄₁	semidirect
292. #1999	C₂×C₄₁	semidirect
293. #1970	C₂×C₄₁	semidirect
294. #1942	C₂×C₄₁	semidirect
295. #1879	C₂×C₄₁	semidirect
296. C₈×C₂²⋊C₄	C₂×C₄₁	semidirect
338. C₄₁	#25414	direct (N × H)
355. C₂×D₈	D₄×C₄₁	semidirect
385. #107	D₄×C₄₁	semidirect
467. C₂²⋊C₄	D₈×C₄₁	semidirect
541. C₈	#121×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×#493	2
C₂×C₄₁×#466	2
C₂×C₄×D₈×C₄₁	2
C₄₁×#2428	2
C₄₁×#2041	2
C₄₁×#1999	2
C₄₁×#1970	2
C₄₁×#1942	2
C₄₁×#1879	2
C₈×C₂²⋊C₄×C₄₁	2
#25414	41

Subgroups — C41×#25414 #23801615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25414 #23801615