Subgroups — C₄₁×#35051 #23811252

Order 10496.

3078 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#525	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2847	C₂	1	4	yes	maximal, complemented
3	C₄₁×#2659	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2656	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2639	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2564	C₂	1	4	yes	maximal, complemented
7	C₄₁×#2543	C₂	1	4	yes	maximal, complemented
8	C₄₁×#2498	C₂	1	4	yes	maximal, complemented
9	C₄₁×#2430	C₂	1	4	yes	maximal, complemented
10	C₄₁×#2325	C₂	1	4	yes	maximal, complemented
11	C₂²×#95×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#525	—	2	16	no	—
16	C₂×#123×C₄₁	C₂²	1	4	yes	—
17	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
19	C₂×#121×C₄₁	C₂²	1	2	yes	—
20	C₂×#121×C₄₁	C₂²	1	4	yes	—
21	C₂×#121×C₄₁	C₂²	1	2	yes	—
22	C₂×#121×C₄₁	C₂²	1	4	yes	—
23	C₂×#121×C₄₁	C₂²	1	4	yes	—
24	C₂×#120×C₄₁	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
27	C₂×#117×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#400	C₂²	1	4	yes	complemented
29	C₄₁×#399	C₂²	1	4	yes	complemented
30	C₄₁×#398	C₂²	1	4	yes	complemented
31	C₄₁×#397	C₂²	1	4	yes	complemented
32	C₄₁×#395	C₂²	1	4	yes	complemented
33	C₄₁×#394	C₂²	1	4	yes	complemented
34	C₄₁×#393	C₂²	1	4	yes	complemented
35	C₄₁×#392	C₂²	1	4	yes	complemented
36	C₄₁×#388	C₂²	1	8	yes	complemented
37	C₄₁×#387	C₂²	1	8	yes	complemented
38	C₄₁×#386	C₂²	1	8	yes	—
39	C₄₁×#386	C₂²	1	8	yes	—
40	C₄₁×#386	C₂²	1	8	yes	—
41	C₄₁×#386	C₂²	1	8	yes	complemented
42	C₄₁×#385	C₂²	1	8	yes	complemented
43	C₄₁×#380	C₂²	1	4	yes	—
44	C₄₁×#380	C₂²	1	4	yes	—
45	C₄₁×#380	C₂²	1	4	yes	—
46	C₂×#95×C₄₁	C₂²	1	4	yes	—
47	C₂×#95×C₄₁	C₂²	1	2	yes	—
48	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
50	C₂×#95×C₄₁	C₂²	1	4	yes	—
51	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
52	C₂×#41×C₄₁	—	2	8	no	—
53	C₂×#41×C₄₁	—	4	8	no	—
54	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
55	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
56	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
57	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
58	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
59	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₁	—	2	8	no	—
61	C₂³×C₄×C₄₁	—	4	4	no	—
62	C₂³×C₄×C₄₁	—	4	4	no	—
63	C₂³×C₄×C₄₁	—	4	4	no	—
64	C₂³×C₄×C₄₁	D₄	1	8	yes	complemented
65	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
66	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
67	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
69	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
70	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
74	#123×C₄₁	—	2	16	no	—
75	C₂²⋊Q₈×C₄₁	—	2	8	no	—
76	C₂²⋊Q₈×C₄₁	—	2	8	no	—
77	#121×C₄₁	—	2	8	no	—
78	#121×C₄₁	—	2	8	no	—
79	#121×C₄₁	—	2	16	no	—
80	#121×C₄₁	—	4	8	no	—
81	#121×C₄₁	—	4	8	no	—
82	#120×C₄₁	—	2	16	no	—
83	C₄×D₄×C₄₁	—	2	16	no	—
84	C₄×D₄×C₄₁	—	2	16	no	—
85	#117×C₄₁	—	2	8	no	—
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
101	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
102	#95×C₄₁	C₂³	1	8	yes	—
103	#95×C₄₁	C₂³	1	4	yes	—
104	#95×C₄₁	C₂³	1	4	yes	—
105	#95×C₄₁	C₂³	1	8	yes	—
106	#95×C₄₁	C₂³	1	8	yes	—
107	#95×C₄₁	C₂³	1	8	yes	—
108	C₂⁴×C₄₁	—	2	4	no	—
109	C₂⁴×C₄₁	—	2	2	no	—
110	C₂⁴×C₄₁	—	2	4	no	—
111	C₂⁴×C₄₁	—	2	2	no	—
112	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
113	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
114	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
115	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
116	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
117	#41×C₄₁	—	4	32	no	—
118	C₂×Q₈×C₄₁	—	2	4	no	—
119	C₂×Q₈×C₄₁	—	4	4	no	—
120	C₂×D₄×C₄₁	—	2	8	no	—
121	C₂×D₄×C₄₁	—	2	8	no	—
122	C₂×D₄×C₄₁	—	2	8	no	—
123	C₂×D₄×C₄₁	—	2	16	no	—
124	C₂×D₄×C₄₁	—	2	8	no	—
125	C₂×D₄×C₄₁	—	2	16	no	—
126	C₂×D₄×C₄₁	—	2	8	no	—
127	C₂×D₄×C₄₁	—	2	4	no	—
128	C₂×D₄×C₄₁	—	2	8	no	—
129	C₂×D₄×C₄₁	—	4	4	no	—
130	C₂×D₄×C₄₁	—	4	4	no	—
131	C₂×D₄×C₄₁	—	4	4	no	—
132	C₂²×C₄×C₄₁	—	2	8	no	—
133	C₂²×C₄×C₄₁	—	2	4	no	—
134	C₂²×C₄×C₄₁	—	2	8	no	—
135	C₂²×C₄×C₄₁	—	2	8	no	—
136	C₂²×C₄×C₄₁	—	2	8	no	—
137	C₂²×C₄×C₄₁	—	2	8	no	—
138	C₂²×C₄×C₄₁	—	2	8	no	—
139	C₂²×C₄×C₄₁	—	4	16	no	—
140	C₂²×C₄×C₄₁	—	4	2	no	—
141	C₂²×C₄×C₄₁	—	4	2	no	—
142	C₂²×C₄×C₄₁	—	4	4	no	—
143	C₂²×C₄×C₄₁	—	4	4	no	—
144	C₂²×C₄×C₄₁	—	4	2	no	—
145	C₂²×C₄×C₄₁	—	4	4	no	—
146	C₂²×C₄×C₄₁	—	4	2	no	—
147	C₂²×C₄×C₄₁	—	4	2	no	—
148	C₂²×C₄×C₄₁	—	4	2	no	—
149	C₂²×C₄×C₄₁	—	4	8	no	—
150	C₂²×C₄×C₄₁	—	4	32	no	—
151	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
152	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₄₁	#41	1	8	yes	complemented
156	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
163	C₄⋊C₄×C₄₁	—	2	4	no	—
164	C₄⋊C₄×C₄₁	—	2	4	no	—
165	C₄⋊C₄×C₄₁	—	2	8	no	—
166	C₄⋊C₄×C₄₁	—	2	8	no	—
167	C₄⋊C₄×C₄₁	—	2	8	no	—
168	C₄⋊C₄×C₄₁	—	4	4	no	—
169	C₄⋊C₄×C₄₁	—	4	4	no	—
170	C₂²⋊C₄×C₄₁	—	2	8	no	—
171	C₂²⋊C₄×C₄₁	—	2	8	no	—
172	C₂²⋊C₄×C₄₁	—	2	8	no	—
173	C₂²⋊C₄×C₄₁	—	2	8	no	—
174	C₂²⋊C₄×C₄₁	—	2	8	no	—
175	C₂²⋊C₄×C₄₁	—	2	16	no	—
176	C₂²⋊C₄×C₄₁	—	4	8	no	—
177	C₂²⋊C₄×C₄₁	—	4	8	no	—
178	C₄²×C₄₁	—	2	8	no	—
179	C₂³×C₄₁	—	2	16	no	—
180	C₂³×C₄₁	—	2	16	no	—
181	C₂³×C₄₁	—	2	8	no	—
182	C₂³×C₄₁	—	2	8	no	—
183	C₂³×C₄₁	—	2	8	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	2	no	—
186	C₂³×C₄₁	—	2	2	no	—
187	C₂³×C₄₁	—	2	2	no	—
188	C₂³×C₄₁	—	2	1	no	—
189	C₂³×C₄₁	—	2	1	no	—
190	C₂³×C₄₁	—	2	1	no	—
191	C₂³×C₄₁	—	2	1	no	—
192	C₂³×C₄₁	—	2	4	no	—
193	C₂³×C₄₁	—	2	8	no	—
194	C₂³×C₄₁	—	2	4	no	—
195	C₂³×C₄₁	—	2	8	no	—
196	C₂³×C₄₁	—	2	4	no	—
197	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
198	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
199	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
200	C₂³×C₄₁	C₂×#41	1	4	yes	—
201	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
202	C₂³×C₄₁	H(5,𝔽₂)	1	2	yes	—
203	C₂³×C₄₁	2₋¹⁺⁴	1	2	yes	—
204	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
205	Q₈×C₄₁	—	4	8	no	—
206	D₄×C₄₁	—	4	8	no	—
207	D₄×C₄₁	—	4	16	no	—
208	D₄×C₄₁	—	4	16	no	—
209	D₄×C₄₁	—	4	16	no	—
210	D₄×C₄₁	—	8	8	no	—
211	C₂×C₄×C₄₁	—	2	16	no	—
212	C₂×C₄×C₄₁	—	2	4	no	—
213	C₂×C₄×C₄₁	—	2	4	no	—
214	C₂×C₄×C₄₁	—	2	4	no	—
215	C₂×C₄×C₄₁	—	2	4	no	—
216	C₂×C₄×C₄₁	—	2	4	no	—
217	C₂×C₄×C₄₁	—	2	4	no	—
218	C₂×C₄×C₄₁	—	2	4	no	—
219	C₂×C₄×C₄₁	—	2	8	no	—
220	C₂×C₄×C₄₁	—	2	4	no	—
221	C₂×C₄×C₄₁	—	2	4	no	—
222	C₂×C₄×C₄₁	—	2	4	no	—
223	C₂×C₄×C₄₁	—	2	4	no	—
224	C₂×C₄×C₄₁	—	2	8	no	—
225	C₂×C₄×C₄₁	—	2	4	no	—
226	C₂×C₄×C₄₁	—	4	4	no	—
227	C₂×C₄×C₄₁	—	4	8	no	—
228	C₂×C₄×C₄₁	—	4	4	no	—
229	C₂×C₄×C₄₁	—	4	8	no	—
230	C₂×C₄×C₄₁	—	4	16	no	—
231	C₂×C₄×C₄₁	—	4	16	no	—
232	C₂×C₄×C₄₁	—	4	16	no	—
233	C₂×C₄×C₄₁	—	4	8	no	—
234	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
236	C₂×C₄×C₄₁	C₂×#41	1	8	yes	—
237	#35051	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂²×C₄₁	—	2	32	no	—
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	—	2	4	no	—
246	C₂²×C₄₁	—	2	4	no	—
247	C₂²×C₄₁	—	2	4	no	—
248	C₂²×C₄₁	—	2	4	no	—
249	C₂²×C₄₁	—	2	4	no	—
250	C₂²×C₄₁	—	2	4	no	—
251	C₂²×C₄₁	—	4	4	no	—
252	C₂²×C₄₁	—	4	4	no	—
253	C₂²×C₄₁	—	4	4	no	—
254	C₂²×C₄₁	—	4	8	no	—
255	C₂²×C₄₁	—	4	8	no	—
256	C₂²×C₄₁	#532	1	4	yes	—
257	C₂²×C₄₁	#534	1	4	yes	—
258	C₂²×C₄₁	#537	1	4	yes	—
259	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
260	C₂²×C₄₁	C₂²×#41	1	2	yes	—
261	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
262	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
264	C₄×C₄₁	—	2	4	no	—
265	C₄×C₄₁	—	2	4	no	—
266	C₄×C₄₁	—	2	8	no	—
267	C₄×C₄₁	—	4	4	no	—
268	C₄×C₄₁	—	4	4	no	—
269	C₄×C₄₁	—	4	4	no	—
270	C₄×C₄₁	—	4	4	no	—
271	C₂×#525	C₂×C₄₁	1	2	yes	complemented
272	#2847	C₂×C₄₁	1	4	yes	complemented
273	#2659	C₂×C₄₁	1	1	yes	characteristic, complemented
274	#2656	C₂×C₄₁	1	1	yes	characteristic, complemented
275	#2639	C₂×C₄₁	1	2	yes	complemented
276	#2564	C₂×C₄₁	1	4	yes	complemented
277	#2543	C₂×C₄₁	1	4	yes	complemented
278	#2498	C₂×C₄₁	1	4	yes	complemented
279	#2430	C₂×C₄₁	1	4	yes	complemented
280	#2325	C₂×C₄₁	1	4	yes	complemented
281	C₂²×#95	C₂×C₄₁	1	1	yes	characteristic, complemented
282	C₂×C₄₁	—	2	4	no	—
283	C₂×C₄₁	—	2	4	no	—
284	C₂×C₄₁	—	2	4	no	—
285	C₂×C₄₁	—	8	4	no	—
286	C₂×C₄₁	C₂×#532	1	1	yes	characteristic
287	C₂×C₄₁	C₂×#534	1	1	yes	characteristic
288	C₂×C₄₁	C₂×#537	1	1	yes	characteristic
289	C₂×C₄₁	#3490	1	2	yes	—
290	C₂×C₄₁	#3492	1	2	yes	—
291	C₂²×#41	C₂²×C₄₁	1	2	yes	—
292	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
293	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
294	#525	—	2	16	no	—
295	C₂×#123	C₂²×C₄₁	1	4	yes	—
296	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
297	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
298	C₂×#121	C₂²×C₄₁	1	4	yes	—
299	C₂×#121	C₂²×C₄₁	1	2	yes	—
300	C₂×#121	C₂²×C₄₁	1	2	yes	—
301	C₂×#121	C₂²×C₄₁	1	4	yes	—
302	C₂×#121	C₂²×C₄₁	1	4	yes	—
303	C₂×#120	C₂²×C₄₁	1	4	yes	—
304	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
305	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
306	C₂×#117	C₂²×C₄₁	1	2	yes	—
307	#400	C₂²×C₄₁	1	4	yes	complemented
308	#399	C₂²×C₄₁	1	4	yes	complemented
309	#398	C₂²×C₄₁	1	4	yes	complemented
310	#397	C₂²×C₄₁	1	4	yes	complemented
311	#395	C₂²×C₄₁	1	4	yes	complemented
312	#394	C₂²×C₄₁	1	4	yes	complemented
313	#393	C₂²×C₄₁	1	4	yes	complemented
314	#392	C₂²×C₄₁	1	4	yes	complemented
315	#388	C₂²×C₄₁	1	8	yes	complemented
316	#387	C₂²×C₄₁	1	8	yes	complemented
317	#386	C₂²×C₄₁	1	8	yes	—
318	#386	C₂²×C₄₁	1	8	yes	—
319	#386	C₂²×C₄₁	1	8	yes	—
320	#386	C₂²×C₄₁	1	8	yes	complemented
321	#385	C₂²×C₄₁	1	8	yes	complemented
322	#380	C₂²×C₄₁	1	4	yes	—
323	#380	C₂²×C₄₁	1	4	yes	—
324	#380	C₂²×C₄₁	1	4	yes	—
325	C₂×#95	C₂²×C₄₁	1	4	yes	—
326	C₂×#95	C₂²×C₄₁	1	2	yes	—
327	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
328	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
329	C₂×#95	C₂²×C₄₁	1	4	yes	—
330	C₄₁	#35051	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
332	C₂×#41	—	2	8	no	—
333	C₂×#41	—	4	8	no	—
334	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
335	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
336	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
337	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
338	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
339	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
340	C₂³×C₄	—	2	8	no	—
341	C₂³×C₄	—	4	4	no	—
342	C₂³×C₄	—	4	4	no	—
343	C₂³×C₄	—	4	4	no	—
344	C₂³×C₄	D₄×C₄₁	1	8	yes	complemented
345	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
346	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
347	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
348	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
349	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
350	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
352	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
354	#123	—	2	16	no	—
355	C₂²⋊Q₈	—	2	8	no	—
356	C₂²⋊Q₈	—	2	8	no	—
357	#121	—	2	8	no	—
358	#121	—	2	8	no	—
359	#121	—	2	16	no	—
360	#121	—	4	8	no	—
361	#121	—	4	8	no	—
362	#120	—	2	16	no	—
363	C₄×D₄	—	2	16	no	—
364	C₄×D₄	—	2	16	no	—
365	#117	—	2	8	no	—
366	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
381	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
382	#95	C₂³×C₄₁	1	8	yes	—
383	#95	C₂³×C₄₁	1	4	yes	—
384	#95	C₂³×C₄₁	1	4	yes	—
385	#95	C₂³×C₄₁	1	8	yes	—
386	#95	C₂³×C₄₁	1	8	yes	—
387	#95	C₂³×C₄₁	1	8	yes	—
388	C₂⁴	—	2	4	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
393	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
394	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
395	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
396	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
397	#41	—	4	32	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	4	4	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	16	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	16	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂²×C₄	—	2	8	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	4	16	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	8	no	—
430	C₂²×C₄	—	4	32	no	—
431	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
432	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
433	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
434	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
435	C₂²×C₄	#41×C₄₁	1	8	yes	complemented
436	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	4	4	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	16	no	—
456	C₂²⋊C₄	—	4	8	no	—
457	C₂²⋊C₄	—	4	8	no	—
458	C₄²	—	2	8	no	—
459	C₂³	—	2	16	no	—
460	C₂³	—	2	16	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	8	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
478	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
479	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
480	C₂³	C₂×#41×C₄₁	1	4	yes	—
481	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
482	C₂³	H(5,𝔽₂)×C₄₁	1	2	yes	—
483	C₂³	2₋¹⁺⁴×C₄₁	1	2	yes	—
484	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
485	Q₈	—	4	8	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	16	no	—
488	D₄	—	4	16	no	—
489	D₄	—	4	16	no	—
490	D₄	—	8	8	no	—
491	C₂×C₄	—	2	16	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	16	no	—
511	C₂×C₄	—	4	16	no	—
512	C₂×C₄	—	4	16	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
515	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
516	C₂×C₄	C₂×#41×C₄₁	1	8	yes	—
517	C₂²	—	2	32	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	4	8	no	—
534	C₂²	—	4	8	no	—
535	C₂²	C₄₁×#532	1	4	yes	—
536	C₂²	C₄₁×#534	1	4	yes	—
537	C₂²	C₄₁×#537	1	4	yes	—
538	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
539	C₂²	C₂²×#41×C₄₁	1	2	yes	—
540	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
541	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
542	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
543	C₄	—	2	4	no	—
544	C₄	—	2	4	no	—
545	C₄	—	2	8	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	4	no	—
550	C₂	—	2	4	no	—
551	C₂	—	2	4	no	—
552	C₂	—	2	4	no	—
553	C₂	—	8	4	no	—
554	C₂	C₂×C₄₁×#532	1	1	yes	characteristic
555	C₂	C₂×C₄₁×#534	1	1	yes	characteristic
556	C₂	C₂×C₄₁×#537	1	1	yes	characteristic
557	C₂	C₄₁×#3490	1	2	yes	—
558	C₂	C₄₁×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#525	C₂	semidirect
2. C₄₁×#2847	C₂	semidirect
3. C₄₁×#2659	C₂	semidirect
4. C₄₁×#2656	C₂	semidirect
5. C₄₁×#2639	C₂	semidirect
6. C₄₁×#2564	C₂	semidirect
7. C₄₁×#2543	C₂	semidirect
8. C₄₁×#2498	C₂	semidirect
9. C₄₁×#2430	C₂	semidirect
10. C₄₁×#2325	C₂	semidirect
11. C₂²×#95×C₄₁	C₂	semidirect
28. C₄₁×#400	C₂²	semidirect
29. C₄₁×#399	C₂²	semidirect
30. C₄₁×#398	C₂²	semidirect
31. C₄₁×#397	C₂²	semidirect
32. C₄₁×#395	C₂²	semidirect
33. C₄₁×#394	C₂²	semidirect
34. C₄₁×#393	C₂²	semidirect
35. C₄₁×#392	C₂²	semidirect
36. C₄₁×#388	C₂²	semidirect
37. C₄₁×#387	C₂²	semidirect
41. C₄₁×#386	C₂²	semidirect
42. C₄₁×#385	C₂²	semidirect
64. C₂³×C₄×C₄₁	D₄	semidirect
155. C₂²×C₄×C₄₁	#41	semidirect
237. #35051	C₄₁	direct (N × H)
271. C₂×#525	C₂×C₄₁	semidirect
272. #2847	C₂×C₄₁	semidirect
273. #2659	C₂×C₄₁	semidirect
274. #2656	C₂×C₄₁	semidirect
275. #2639	C₂×C₄₁	semidirect
276. #2564	C₂×C₄₁	semidirect
277. #2543	C₂×C₄₁	semidirect
278. #2498	C₂×C₄₁	semidirect
279. #2430	C₂×C₄₁	semidirect
280. #2325	C₂×C₄₁	semidirect
281. C₂²×#95	C₂×C₄₁	semidirect
307. #400	C₂²×C₄₁	semidirect
308. #399	C₂²×C₄₁	semidirect
309. #398	C₂²×C₄₁	semidirect
310. #397	C₂²×C₄₁	semidirect
311. #395	C₂²×C₄₁	semidirect
312. #394	C₂²×C₄₁	semidirect
313. #393	C₂²×C₄₁	semidirect
314. #392	C₂²×C₄₁	semidirect
315. #388	C₂²×C₄₁	semidirect
316. #387	C₂²×C₄₁	semidirect
320. #386	C₂²×C₄₁	semidirect
321. #385	C₂²×C₄₁	semidirect
330. C₄₁	#35051	direct (N × H)
344. C₂³×C₄	D₄×C₄₁	semidirect
435. C₂²×C₄	#41×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×#525	2
C₄₁×#2847	2
C₄₁×#2659	2
C₄₁×#2656	2
C₄₁×#2639	2
C₄₁×#2564	2
C₄₁×#2543	2
C₄₁×#2498	2
C₄₁×#2430	2
C₄₁×#2325	2
C₂²×#95×C₄₁	2
#35051	41

Subgroups — C41×#35051 #23811252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#35051 #23811252