Subgroups — C₄₁×#22181 #23798382

Order 10496.

1062 conjugacy classes of subgroups.

The subgroup lattice has 476 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
2	C₄×#121×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1925	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1918	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1893	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1879	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1862	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#121×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₄₁	—	2	2	no	—
15	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#466	C₄	1	8	yes	complemented
18	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₄₁	C₂²	1	2	yes	—
22	C₂×#102×C₄₁	C₂²	1	2	yes	—
23	C₂×#102×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#390	C₂²	1	2	yes	—
25	C₄₁×#389	C₂²	1	2	yes	—
26	C₄₁×#388	—	2	2	no	—
27	C₄₁×#386	—	2	2	no	—
28	C₄₁×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
31	C₄₁×#340	C₂²	1	2	yes	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₁	—	2	2	no	—
39	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
42	C₂×D₈×C₄₁	—	4	1	no	—
43	C₂×D₈×C₄₁	—	4	1	no	—
44	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	complemented
45	C₂²×C₈×C₄₁	—	2	2	no	—
46	C₂²×C₈×C₄₁	—	4	1	no	—
47	C₂²×C₈×C₄₁	—	4	1	no	—
48	C₂²×C₈×C₄₁	—	4	1	no	—
49	C₂²×C₈×C₄₁	—	4	1	no	—
50	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
51	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
54	#121×C₄₁	—	2	4	no	—
55	#121×C₄₁	C₂×C₄	1	8	yes	complemented
56	C₄×D₄×C₄₁	—	4	2	no	—
57	C₄×D₄×C₄₁	—	4	2	no	—
58	C₄×D₄×C₄₁	—	4	8	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	—	4	1	no	—
70	C₂×C₄²×C₄₁	—	4	1	no	—
71	C₂×C₄²×C₄₁	D₄	1	2	yes	—
72	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
73	#107×C₄₁	—	4	1	no	—
74	#107×C₄₁	—	4	1	no	—
75	#107×C₄₁	C₂×C₄	1	4	yes	complemented
76	#102×C₄₁	—	4	2	no	—
77	#102×C₄₁	—	4	2	no	—
78	#102×C₄₁	C₂×C₄	1	8	yes	complemented
79	#95×C₄₁	—	2	2	no	—
80	#95×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	2	no	—
82	C₂⁴×C₄₁	—	2	2	no	—
83	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
84	C₂×D₄×C₄₁	—	2	8	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	2	no	—
90	C₂×D₄×C₄₁	—	4	4	no	—
91	C₂×D₄×C₄₁	—	4	4	no	—
92	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₁	—	2	1	no	—
94	C₂²×C₄×C₄₁	—	2	1	no	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	—	2	1	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	4	1	no	—
102	C₂²×C₄×C₄₁	—	4	1	no	—
103	C₂²×C₄×C₄₁	—	4	1	no	—
104	C₂²×C₄×C₄₁	—	4	1	no	—
105	C₂²×C₄×C₄₁	—	4	4	no	—
106	C₂²×C₄×C₄₁	—	4	4	no	—
107	C₂²×C₄×C₄₁	—	4	4	no	—
108	C₂²×C₄×C₄₁	D₈	1	4	yes	complemented
109	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₁	#41	1	2	yes	—
114	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
115	D₈×C₄₁	—	4	4	no	—
116	C₂×C₈×C₄₁	—	2	1	no	—
117	C₂×C₈×C₄₁	—	2	1	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	4	4	no	—
124	C₂×C₈×C₄₁	—	4	4	no	—
125	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₄₁	—	2	2	no	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	4	4	no	—
133	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
134	C₂²⋊C₄×C₄₁	—	2	8	no	—
135	C₂²⋊C₄×C₄₁	—	4	4	no	—
136	C₂²⋊C₄×C₄₁	—	4	4	no	—
137	C₂²⋊C₄×C₄₁	—	4	4	no	—
138	C₂²⋊C₄×C₄₁	—	4	4	no	—
139	C₄²×C₄₁	—	2	2	no	—
140	C₄²×C₄₁	—	2	2	no	—
141	C₄²×C₄₁	—	4	2	no	—
142	C₄²×C₄₁	—	4	4	no	—
143	C₂³×C₄₁	—	2	1	no	—
144	C₂³×C₄₁	—	2	1	no	—
145	C₂³×C₄₁	—	2	1	no	—
146	C₂³×C₄₁	—	2	1	no	—
147	C₂³×C₄₁	—	2	4	no	—
148	C₂³×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	—	4	2	no	—
151	C₂³×C₄₁	—	4	2	no	—
152	C₂³×C₄₁	—	4	2	no	—
153	C₂³×C₄₁	—	4	2	no	—
154	C₂³×C₄₁	C₄×D₄	1	2	yes	—
155	C₂³×C₄₁	C₂×D₈	1	2	yes	—
156	C₂³×C₄₁	#135	1	2	yes	—
157	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
158	D₄×C₄₁	—	2	4	no	—
159	D₄×C₄₁	—	2	4	no	—
160	D₄×C₄₁	—	4	16	no	—
161	D₄×C₄₁	—	4	2	no	—
162	D₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	1	no	—
165	C₂×C₄×C₄₁	—	2	1	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	2	4	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	4	4	no	—
176	C₂×C₄×C₄₁	—	4	4	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	8	8	no	—
186	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₄₁	C₂×D₈	1	4	yes	—
188	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
194	C₈×C₄₁	—	2	2	no	—
195	C₈×C₄₁	—	2	2	no	—
196	C₈×C₄₁	—	4	2	no	—
197	#22181	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₁	—	2	2	no	—
199	C₂²×C₄₁	—	2	2	no	—
200	C₂²×C₄₁	—	2	2	no	—
201	C₂²×C₄₁	—	2	2	no	—
202	C₂²×C₄₁	—	2	2	no	—
203	C₂²×C₄₁	—	2	2	no	—
204	C₂²×C₄₁	—	4	4	no	—
205	C₂²×C₄₁	—	4	4	no	—
206	C₂²×C₄₁	—	4	4	no	—
207	C₂²×C₄₁	—	8	2	no	—
208	C₂²×C₄₁	—	8	2	no	—
209	C₂²×C₄₁	—	8	2	no	—
210	C₂²×C₄₁	—	8	2	no	—
211	C₂²×C₄₁	C₄×D₈	1	4	yes	—
212	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₄₁	#534	1	1	yes	characteristic
214	C₂²×C₄₁	#537	1	1	yes	characteristic
215	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
216	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
217	C₂²×C₄₁	#575	1	1	yes	characteristic
218	C₂²×C₄₁	#575	1	1	yes	characteristic
219	C₄×C₄₁	—	2	2	no	—
220	C₄×C₄₁	—	2	4	no	—
221	C₄×C₄₁	—	4	2	no	—
222	C₄×C₄₁	—	4	4	no	—
223	C₄×C₄₁	—	8	2	no	—
224	C₄×C₄₁	—	8	2	no	—
225	C₄×C₄₁	#518	1	1	yes	characteristic
226	C₄×C₄₁	#520	1	1	yes	characteristic
227	C₄×C₄₁	#538	1	1	yes	characteristic
228	C₄×C₄₁	#539	1	1	yes	characteristic
229	C₂×#466	C₂×C₄₁	1	1	yes	characteristic
230	C₄×#121	C₂×C₄₁	1	2	yes	complemented
231	#1925	C₂×C₄₁	1	2	yes	complemented
232	#1918	C₂×C₄₁	1	2	yes	complemented
233	#1893	C₂×C₄₁	1	2	yes	complemented
234	#1879	C₂×C₄₁	1	2	yes	complemented
235	#1862	C₂×C₄₁	1	2	yes	complemented
236	#1808	C₂×C₄₁	1	1	yes	characteristic, complemented
237	C₂×#336	C₂×C₄₁	1	1	yes	characteristic, complemented
238	C₂×C₄₁	—	2	4	no	—
239	C₂×C₄₁	—	8	4	no	—
240	C₂×C₄₁	#2325	1	1	yes	characteristic
241	C₂×C₄₁	C₂×C₄×D₈	1	1	yes	characteristic
242	C₂×C₄₁	#2943	1	1	yes	characteristic
243	C₂×C₄₁	#3186	1	1	yes	characteristic
244	C₂×C₄₁	#3191	1	1	yes	characteristic
245	C₂×C₄₁	#3245	1	1	yes	characteristic
246	C₂×C₄₁	#3250	1	1	yes	characteristic
247	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
250	C₂×#121	C₂²×C₄₁	1	2	yes	—
251	C₂×C₄×D₄	—	2	2	no	—
252	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
253	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
254	#466	C₄×C₄₁	1	8	yes	complemented
255	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
256	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
257	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
258	C₂×#102	C₂²×C₄₁	1	2	yes	—
259	C₂×#102	C₂²×C₄₁	1	2	yes	—
260	C₂×#102	C₂²×C₄₁	1	2	yes	—
261	#390	C₂²×C₄₁	1	2	yes	—
262	#389	C₂²×C₄₁	1	2	yes	—
263	#388	—	2	2	no	—
264	#386	—	2	2	no	—
265	#380	C₂²×C₄₁	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
267	C₄×C₂²⋊C₄	—	2	2	no	—
268	#340	C₂²×C₄₁	1	2	yes	—
269	#340	C₂²×C₄₁	1	2	yes	—
270	#340	C₂²×C₄₁	1	2	yes	—
271	#336	C₂²×C₄₁	1	2	yes	—
272	#336	C₂²×C₄₁	1	2	yes	—
273	C₄₁	#22181	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
278	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
280	C₂×D₈	—	4	1	no	—
281	C₂×D₈	—	4	1	no	—
282	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	complemented
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	4	1	no	—
285	C₂²×C₈	—	4	1	no	—
286	C₂²×C₈	—	4	1	no	—
287	C₂²×C₈	—	4	1	no	—
288	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
289	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
290	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
292	#121	—	2	4	no	—
293	#121	C₂×C₄×C₄₁	1	8	yes	complemented
294	C₄×D₄	—	4	2	no	—
295	C₄×D₄	—	4	2	no	—
296	C₄×D₄	—	4	8	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	4	1	no	—
308	C₂×C₄²	—	4	1	no	—
309	C₂×C₄²	D₄×C₄₁	1	2	yes	—
310	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
311	#107	—	4	1	no	—
312	#107	—	4	1	no	—
313	#107	C₂×C₄×C₄₁	1	4	yes	complemented
314	#102	—	4	2	no	—
315	#102	—	4	2	no	—
316	#102	C₂×C₄×C₄₁	1	8	yes	complemented
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	D₈×C₄₁	1	4	yes	complemented
347	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
351	C₂²×C₄	#41×C₄₁	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
353	D₈	—	4	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	4	no	—
362	C₂×C₈	—	4	4	no	—
363	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
364	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	2	no	—
380	C₄²	—	4	4	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	C₄×D₄×C₄₁	1	2	yes	—
393	C₂³	C₂×D₈×C₄₁	1	2	yes	—
394	C₂³	#135×C₄₁	1	2	yes	—
395	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
396	D₄	—	2	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	4	16	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	8	no	—
424	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
425	C₂×C₄	C₂×D₈×C₄₁	1	4	yes	—
426	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
428	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
429	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
430	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
431	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	C₄×D₈×C₄₁	1	4	yes	—
449	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
450	C₂²	C₄₁×#534	1	1	yes	characteristic
451	C₂²	C₄₁×#537	1	1	yes	characteristic
452	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
453	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
454	C₂²	C₄₁×#575	1	1	yes	characteristic
455	C₂²	C₄₁×#575	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₄₁×#518	1	1	yes	characteristic
463	C₄	C₄₁×#520	1	1	yes	characteristic
464	C₄	C₄₁×#538	1	1	yes	characteristic
465	C₄	C₄₁×#539	1	1	yes	characteristic
466	C₂	—	2	4	no	—
467	C₂	—	8	4	no	—
468	C₂	C₄₁×#2325	1	1	yes	characteristic
469	C₂	C₂×C₄×D₈×C₄₁	1	1	yes	characteristic
470	C₂	C₄₁×#2943	1	1	yes	characteristic
471	C₂	C₄₁×#3186	1	1	yes	characteristic
472	C₂	C₄₁×#3191	1	1	yes	characteristic
473	C₂	C₄₁×#3245	1	1	yes	characteristic
474	C₂	C₄₁×#3250	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#121×C₄₁	C₂	semidirect
3. C₄₁×#1925	C₂	semidirect
4. C₄₁×#1918	C₂	semidirect
5. C₄₁×#1893	C₂	semidirect
6. C₄₁×#1879	C₂	semidirect
7. C₄₁×#1862	C₂	semidirect
8. C₄₁×#1808	C₂	semidirect
9. C₂×C₄₁×#336	C₂	semidirect
17. C₄₁×#466	C₄	semidirect
44. C₂×D₈×C₄₁	C₂×C₄	semidirect
50. C₂²×C₈×C₄₁	C₂×C₄	semidirect
55. #121×C₄₁	C₂×C₄	semidirect
75. #107×C₄₁	C₂×C₄	semidirect
78. #102×C₄₁	C₂×C₄	semidirect
108. C₂²×C₄×C₄₁	D₈	semidirect
197. #22181	C₄₁	direct (N × H)
230. C₄×#121	C₂×C₄₁	semidirect
231. #1925	C₂×C₄₁	semidirect
232. #1918	C₂×C₄₁	semidirect
233. #1893	C₂×C₄₁	semidirect
234. #1879	C₂×C₄₁	semidirect
235. #1862	C₂×C₄₁	semidirect
236. #1808	C₂×C₄₁	semidirect
237. C₂×#336	C₂×C₄₁	semidirect
254. #466	C₄×C₄₁	semidirect
273. C₄₁	#22181	direct (N × H)
282. C₂×D₈	C₂×C₄×C₄₁	semidirect
288. C₂²×C₈	C₂×C₄×C₄₁	semidirect
293. #121	C₂×C₄×C₄₁	semidirect
313. #107	C₂×C₄×C₄₁	semidirect
316. #102	C₂×C₄×C₄₁	semidirect
346. C₂²×C₄	D₈×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
C₄×#121×C₄₁	2
C₄₁×#1925	2
C₄₁×#1918	2
C₄₁×#1893	2
C₄₁×#1879	2
C₄₁×#1862	2
C₄₁×#1808	2
C₂×C₄₁×#336	2
#22181	41

Subgroups — C41×#22181 #23798382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22181 #23798382