Subgroups — C₄₁×#61430 #23837631

Order 10496.

1870 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3480	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3365	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#3339	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3304	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3301	C₂	1	4	yes	maximal, complemented
9	C₄₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#3285	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3168	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3103	C₂	1	2	yes	maximal, complemented
14	C₄₁×#3102	C₂	1	4	yes	maximal, complemented
15	C₈×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#135×C₄₁	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₄₁	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#559	—	2	2	no	—
21	C₄₁×#559	C₂²	1	2	yes	—
22	C₄₁×#557	C₂²	1	2	yes	—
23	C₄₁×#556	—	2	2	no	—
24	C₄₁×#556	C₂²	1	2	yes	—
25	C₄₁×#553	—	2	4	no	—
26	C₄₁×#553	C₂²	1	4	yes	—
27	C₄₁×#550	C₂²	1	2	yes	—
28	C₄₁×#548	C₂²	1	4	yes	—
29	C₄₁×#532	—	2	2	no	—
30	C₄₁×#532	C₂²	1	2	yes	—
31	C₄₁×#529	—	2	4	no	—
32	C₄₁×#529	C₂²	1	4	yes	—
33	C₄×#41×C₄₁	—	2	2	no	—
34	C₄×#41×C₄₁	C₂²	1	4	yes	—
35	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
37	C₄₁×#500	C₂²	1	1	yes	characteristic
38	C₄₁×#499	C₂²	1	2	yes	—
39	C₄₁×#495	C₂²	1	2	yes	—
40	C₄₁×#493	C₂²	1	1	yes	characteristic
41	C₄₁×#488	C₂²	1	4	yes	—
42	C₄₁×#486	C₂²	1	2	yes	—
43	C₄₁×#485	C₂²	1	4	yes	—
44	C₄₁×#482	C₂²	1	4	yes	—
45	C₄₁×#481	C₂²	1	4	yes	—
46	C₄₁×#479	C₂²	1	4	yes	—
47	C₄₁×#478	C₂²	1	4	yes	—
48	C₄₁×#475	C₂²	1	2	yes	—
49	C₄₁×#475	C₂²	1	2	yes	—
50	C₄₁×#467	C₂²	1	2	yes	—
51	C₄₁×#466	C₂²	1	2	yes	—
52	C₄₁×#466	C₂²	1	2	yes	—
53	C₄₁×#466	C₂²	1	2	yes	—
54	C₄₁×#465	C₂²	1	4	yes	—
55	C₄₁×#464	C₂²	1	4	yes	—
56	C₄₁×#463	C₂²	1	4	yes	—
57	C₄₁×#460	C₂²	1	2	yes	—
58	C₄₁×#460	C₂²	1	2	yes	—
59	C₄₁×#452	C₂²	1	4	yes	—
60	C₄₁×#449	C₂²	1	4	yes	—
61	C₄₁×#448	C₂²	1	4	yes	—
62	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
64	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
65	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
66	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
67	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
68	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
69	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
70	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
71	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
72	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
73	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
74	C₄×D₈×C₄₁	C₂²	1	2	yes	—
75	C₄×D₈×C₄₁	C₂²	1	2	yes	—
76	C₄×D₈×C₄₁	C₂²	1	2	yes	—
77	C₈×D₄×C₄₁	C₂²	1	2	yes	—
78	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₄₁	C₂²	1	2	yes	—
80	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
81	C₄₁×#431	C₂²	1	2	yes	—
82	C₄₁×#431	C₂²	1	1	yes	characteristic
83	C₄₁×#427	C₂²	1	2	yes	—
84	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
85	C₄₁×#416	C₂²	1	4	yes	—
86	C₂×#103×C₄₁	C₂²	1	2	yes	—
87	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
89	C₂×#41×C₄₁	—	2	2	no	—
90	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
91	C₂×#41×C₄₁	C₂³	1	4	yes	—
92	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
93	#135×C₄₁	—	2	8	no	—
94	C₂×Q₁₆×C₄₁	—	2	4	no	—
95	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
97	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
100	C₂×D₈×C₄₁	C₂³	1	2	yes	—
101	C₂×D₈×C₄₁	C₂³	1	2	yes	—
102	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₄₁	—	2	2	no	—
107	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
108	#127×C₄₁	—	2	2	no	—
109	#127×C₄₁	C₂³	1	2	yes	—
110	#126×C₄₁	—	2	4	no	—
111	#126×C₄₁	—	2	4	no	—
112	#126×C₄₁	—	2	4	no	—
113	#125×C₄₁	—	2	4	no	—
114	#125×C₄₁	C₂³	1	4	yes	—
115	#124×C₄₁	—	2	2	no	—
116	#124×C₄₁	—	2	2	no	—
117	#124×C₄₁	—	2	4	no	—
118	#124×C₄₁	—	2	2	no	—
119	#124×C₄₁	C₂³	1	4	yes	—
120	#123×C₄₁	—	2	4	no	—
121	#123×C₄₁	—	2	4	no	—
122	#123×C₄₁	—	2	4	no	—
123	C₂²⋊Q₈×C₄₁	—	2	4	no	—
124	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
125	#121×C₄₁	—	2	4	no	—
126	#121×C₄₁	—	2	4	no	—
127	#121×C₄₁	—	2	2	no	—
128	#121×C₄₁	—	2	4	no	—
129	#121×C₄₁	C₂³	1	4	yes	—
130	#121×C₄₁	C₂³	1	4	yes	—
131	C₄×Q₈×C₄₁	—	2	2	no	—
132	C₄×Q₈×C₄₁	—	2	2	no	—
133	C₄×Q₈×C₄₁	—	2	2	no	—
134	C₄×Q₈×C₄₁	—	2	2	no	—
135	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
136	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
137	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
138	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
139	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
140	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
141	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₄₁	—	2	4	no	—
143	C₄×D₄×C₄₁	—	2	4	no	—
144	C₄×D₄×C₄₁	—	2	4	no	—
145	C₄×D₄×C₄₁	—	2	2	no	—
146	C₄×D₄×C₄₁	—	2	2	no	—
147	C₄×D₄×C₄₁	—	2	4	no	—
148	C₄×D₄×C₄₁	—	2	4	no	—
149	C₄×D₄×C₄₁	—	2	2	no	—
150	C₄×D₄×C₄₁	D₄	1	2	yes	—
151	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
152	C₄×D₄×C₄₁	C₂³	1	4	yes	—
153	C₄×D₄×C₄₁	C₂³	1	4	yes	—
154	C₄×D₄×C₄₁	C₂³	1	2	yes	—
155	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
156	#117×C₄₁	—	2	4	no	—
157	#117×C₄₁	—	2	4	no	—
158	#117×C₄₁	D₄	1	1	yes	characteristic
159	#117×C₄₁	D₄	1	2	yes	—
160	#117×C₄₁	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₄₁	—	2	2	no	—
164	C₂×C₄²×C₄₁	—	2	4	no	—
165	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
167	#107×C₄₁	C₂³	1	2	yes	—
168	#107×C₄₁	C₂³	1	2	yes	—
169	#107×C₄₁	C₂³	1	1	yes	characteristic
170	#107×C₄₁	C₂³	1	1	yes	characteristic
171	#107×C₄₁	C₂³	1	2	yes	—
172	#106×C₄₁	C₂³	1	4	yes	—
173	#106×C₄₁	C₂³	1	4	yes	—
174	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
178	#103×C₄₁	C₂³	1	2	yes	—
179	#103×C₄₁	C₂³	1	2	yes	—
180	#103×C₄₁	C₂³	1	2	yes	—
181	#103×C₄₁	C₂³	1	2	yes	—
182	#103×C₄₁	C₂³	1	4	yes	—
183	#103×C₄₁	C₂³	1	4	yes	—
184	#102×C₄₁	C₂³	1	4	yes	—
185	#102×C₄₁	C₂³	1	4	yes	—
186	#102×C₄₁	C₂³	1	4	yes	—
187	#102×C₄₁	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
191	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₄₁	C₂³	1	2	yes	—
195	C₄×C₈×C₄₁	C₂³	1	2	yes	—
196	C₄×C₈×C₄₁	C₂³	1	2	yes	—
197	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
198	#41×C₄₁	—	2	4	no	—
199	#41×C₄₁	—	2	8	no	—
200	#41×C₄₁	—	4	4	no	—
201	#41×C₄₁	—	4	8	no	—
202	C₂×Q₈×C₄₁	—	2	2	no	—
203	C₂×Q₈×C₄₁	—	2	2	no	—
204	C₂×Q₈×C₄₁	—	2	4	no	—
205	C₂×Q₈×C₄₁	—	4	2	no	—
206	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₄₁	—	2	4	no	—
210	C₂×D₄×C₄₁	—	2	4	no	—
211	C₂×D₄×C₄₁	—	2	4	no	—
212	C₂×D₄×C₄₁	—	2	2	no	—
213	C₂×D₄×C₄₁	—	2	2	no	—
214	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₄₁	—	2	2	no	—
218	C₂²×C₄×C₄₁	—	2	2	no	—
219	C₂²×C₄×C₄₁	—	2	4	no	—
220	C₂²×C₄×C₄₁	—	2	4	no	—
221	C₂²×C₄×C₄₁	—	2	4	no	—
222	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
228	Q₁₆×C₄₁	—	2	4	no	—
229	Q₁₆×C₄₁	—	2	2	no	—
230	Q₁₆×C₄₁	#41	1	4	yes	complemented
231	SD₁₆×C₄₁	—	2	8	no	—
232	SD₁₆×C₄₁	—	4	4	no	—
233	D₈×C₄₁	—	2	4	no	—
234	D₈×C₄₁	—	4	2	no	—
235	C₂×C₈×C₄₁	—	2	2	no	—
236	C₂×C₈×C₄₁	—	2	4	no	—
237	C₂×C₈×C₄₁	—	4	1	no	—
238	C₂×C₈×C₄₁	—	4	2	no	—
239	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
242	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
243	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
245	C₄⋊C₄×C₄₁	—	2	2	no	—
246	C₄⋊C₄×C₄₁	—	2	2	no	—
247	C₄⋊C₄×C₄₁	—	2	2	no	—
248	C₄⋊C₄×C₄₁	—	2	2	no	—
249	C₄⋊C₄×C₄₁	—	2	2	no	—
250	C₄⋊C₄×C₄₁	—	2	4	no	—
251	C₄⋊C₄×C₄₁	—	2	4	no	—
252	C₄⋊C₄×C₄₁	—	2	4	no	—
253	C₄⋊C₄×C₄₁	—	2	2	no	—
254	C₄⋊C₄×C₄₁	—	2	4	no	—
255	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₄₁	—	2	4	no	—
263	C₂²⋊C₄×C₄₁	—	2	4	no	—
264	C₂²⋊C₄×C₄₁	—	2	4	no	—
265	C₂²⋊C₄×C₄₁	—	2	4	no	—
266	C₂²⋊C₄×C₄₁	—	2	4	no	—
267	C₂²⋊C₄×C₄₁	—	2	4	no	—
268	C₂²⋊C₄×C₄₁	—	2	4	no	—
269	C₂²⋊C₄×C₄₁	—	2	4	no	—
270	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
273	C₄²×C₄₁	—	2	4	no	—
274	C₄²×C₄₁	—	2	4	no	—
275	C₄²×C₄₁	—	2	2	no	—
276	C₄²×C₄₁	—	2	2	no	—
277	C₄²×C₄₁	—	2	2	no	—
278	C₄²×C₄₁	—	2	2	no	—
279	C₄²×C₄₁	C₂×D₄	1	2	yes	—
280	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₄₁	C₂×D₄	1	2	yes	—
282	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₄₁	C₂⁴	1	2	yes	—
284	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
286	C₂³×C₄₁	—	2	4	no	—
287	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
288	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₄₁	—	2	2	no	—
290	Q₈×C₄₁	—	2	2	no	—
291	Q₈×C₄₁	—	2	2	no	—
292	Q₈×C₄₁	—	2	2	no	—
293	Q₈×C₄₁	—	4	4	no	—
294	Q₈×C₄₁	—	4	4	no	—
295	Q₈×C₄₁	C₂×#41	1	4	yes	—
296	D₄×C₄₁	—	2	4	no	—
297	D₄×C₄₁	—	2	2	no	—
298	D₄×C₄₁	—	2	4	no	—
299	D₄×C₄₁	—	2	4	no	—
300	D₄×C₄₁	—	4	8	no	—
301	D₄×C₄₁	—	4	8	no	—
302	D₄×C₄₁	—	4	4	no	—
303	D₄×C₄₁	—	8	2	no	—
304	D₄×C₄₁	—	8	4	no	—
305	C₂×C₄×C₄₁	—	2	2	no	—
306	C₂×C₄×C₄₁	—	2	4	no	—
307	C₂×C₄×C₄₁	—	2	1	no	—
308	C₂×C₄×C₄₁	—	2	2	no	—
309	C₂×C₄×C₄₁	—	2	1	no	—
310	C₂×C₄×C₄₁	—	2	2	no	—
311	C₂×C₄×C₄₁	—	2	2	no	—
312	C₂×C₄×C₄₁	—	2	2	no	—
313	C₂×C₄×C₄₁	—	2	4	no	—
314	C₂×C₄×C₄₁	—	2	2	no	—
315	C₂×C₄×C₄₁	—	4	2	no	—
316	C₂×C₄×C₄₁	—	4	1	no	—
317	C₂×C₄×C₄₁	—	4	8	no	—
318	C₂×C₄×C₄₁	—	4	4	no	—
319	C₂×C₄×C₄₁	—	4	8	no	—
320	C₂×C₄×C₄₁	—	8	4	no	—
321	C₂×C₄×C₄₁	—	8	2	no	—
322	C₂×C₄×C₄₁	#135	1	4	yes	complemented
323	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
332	C₈×C₄₁	—	2	2	no	—
333	C₈×C₄₁	—	2	1	no	—
334	C₈×C₄₁	—	2	1	no	—
335	C₈×C₄₁	—	2	1	no	—
336	C₈×C₄₁	—	2	2	no	—
337	C₈×C₄₁	C₂×#41	1	2	yes	—
338	#61430	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂²×C₄₁	—	2	1	no	—
340	C₂²×C₄₁	—	2	1	no	—
341	C₂²×C₄₁	—	2	2	no	—
342	C₂²×C₄₁	—	2	2	no	—
343	C₂²×C₄₁	—	2	2	no	—
344	C₂²×C₄₁	—	4	4	no	—
345	C₂²×C₄₁	—	4	4	no	—
346	C₂²×C₄₁	—	4	4	no	—
347	C₂²×C₄₁	C₂×#135	1	2	yes	—
348	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
349	C₄×C₄₁	—	2	1	no	—
350	C₄×C₄₁	—	2	2	no	—
351	C₄×C₄₁	—	2	1	no	—
352	C₄×C₄₁	—	2	2	no	—
353	C₄×C₄₁	—	2	1	no	—
354	C₄×C₄₁	—	2	4	no	—
355	C₄×C₄₁	—	2	2	no	—
356	C₄×C₄₁	—	4	2	no	—
357	C₄×C₄₁	—	4	2	no	—
358	C₄×C₄₁	—	4	2	no	—
359	C₄×C₄₁	—	4	4	no	—
360	C₄×C₄₁	C₂×#135	1	2	yes	—
361	C₄×C₄₁	C₂×#135	1	2	yes	—
362	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
363	C₄×C₄₁	#585	1	1	yes	characteristic
364	#3480	C₂×C₄₁	1	2	yes	complemented
365	#3396	C₂×C₄₁	1	1	yes	characteristic, complemented
366	#3383	C₂×C₄₁	1	1	yes	characteristic, complemented
367	#3365	C₂×C₄₁	1	2	yes	complemented
368	#3342	C₂×C₄₁	1	1	yes	characteristic, complemented
369	#3339	C₂×C₄₁	1	2	yes	complemented
370	#3304	C₂×C₄₁	1	2	yes	complemented
371	#3301	C₂×C₄₁	1	4	yes	complemented
372	#3287	C₂×C₄₁	1	1	yes	characteristic, complemented
373	#3285	C₂×C₄₁	1	2	yes	complemented
374	#3169	C₂×C₄₁	1	1	yes	characteristic, complemented
375	#3168	C₂×C₄₁	1	2	yes	complemented
376	#3103	C₂×C₄₁	1	2	yes	complemented
377	#3102	C₂×C₄₁	1	4	yes	complemented
378	C₈×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
379	C₄×#135	C₂×C₄₁	1	2	yes	complemented
380	C₂×C₄×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
381	C₂×C₄₁	—	2	2	no	—
382	C₂×C₄₁	—	4	2	no	—
383	C₂×C₄₁	—	8	4	no	—
384	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
385	C₂×C₄₁	C₂²×#135	1	1	yes	characteristic
386	C₂×C₄₁	#3584	1	1	yes	characteristic
387	C₂×#135	C₂²×C₄₁	1	2	yes	—
388	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
389	#559	—	2	2	no	—
390	#559	C₂²×C₄₁	1	2	yes	—
391	#557	C₂²×C₄₁	1	2	yes	—
392	#556	—	2	2	no	—
393	#556	C₂²×C₄₁	1	2	yes	—
394	#553	—	2	4	no	—
395	#553	C₂²×C₄₁	1	4	yes	—
396	#550	C₂²×C₄₁	1	2	yes	—
397	#548	C₂²×C₄₁	1	4	yes	—
398	#532	—	2	2	no	—
399	#532	C₂²×C₄₁	1	2	yes	—
400	#529	—	2	4	no	—
401	#529	C₂²×C₄₁	1	4	yes	—
402	C₄×#41	—	2	2	no	—
403	C₄×#41	C₂²×C₄₁	1	4	yes	—
404	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
406	#500	C₂²×C₄₁	1	1	yes	characteristic
407	#499	C₂²×C₄₁	1	2	yes	—
408	#495	C₂²×C₄₁	1	2	yes	—
409	#493	C₂²×C₄₁	1	1	yes	characteristic
410	#488	C₂²×C₄₁	1	4	yes	—
411	#486	C₂²×C₄₁	1	2	yes	—
412	#485	C₂²×C₄₁	1	4	yes	—
413	#482	C₂²×C₄₁	1	4	yes	—
414	#481	C₂²×C₄₁	1	4	yes	—
415	#479	C₂²×C₄₁	1	4	yes	—
416	#478	C₂²×C₄₁	1	4	yes	—
417	#475	C₂²×C₄₁	1	2	yes	—
418	#475	C₂²×C₄₁	1	2	yes	—
419	#467	C₂²×C₄₁	1	2	yes	—
420	#466	C₂²×C₄₁	1	2	yes	—
421	#466	C₂²×C₄₁	1	2	yes	—
422	#466	C₂²×C₄₁	1	2	yes	—
423	#465	C₂²×C₄₁	1	4	yes	—
424	#464	C₂²×C₄₁	1	4	yes	—
425	#463	C₂²×C₄₁	1	4	yes	—
426	#460	C₂²×C₄₁	1	2	yes	—
427	#460	C₂²×C₄₁	1	2	yes	—
428	#452	C₂²×C₄₁	1	4	yes	—
429	#449	C₂²×C₄₁	1	4	yes	—
430	#448	C₂²×C₄₁	1	4	yes	—
431	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
432	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
433	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
434	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
435	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
436	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
437	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
438	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
439	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
440	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
441	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
442	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
443	C₄×D₈	C₂²×C₄₁	1	2	yes	—
444	C₄×D₈	C₂²×C₄₁	1	2	yes	—
445	C₄×D₈	C₂²×C₄₁	1	2	yes	—
446	C₈×D₄	C₂²×C₄₁	1	2	yes	—
447	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
448	C₈×D₄	C₂²×C₄₁	1	2	yes	—
449	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
450	#431	C₂²×C₄₁	1	2	yes	—
451	#431	C₂²×C₄₁	1	1	yes	characteristic
452	#427	C₂²×C₄₁	1	2	yes	—
453	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
454	#416	C₂²×C₄₁	1	4	yes	—
455	C₂×#103	C₂²×C₄₁	1	2	yes	—
456	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
457	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
458	C₄₁	#61430	1	1	yes	characteristic, direct product factor, Sylow
459	C₂×#41	—	2	2	no	—
460	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
461	C₂×#41	C₂³×C₄₁	1	4	yes	—
462	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
463	#135	—	2	8	no	—
464	C₂×Q₁₆	—	2	4	no	—
465	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
466	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
467	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
468	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
470	C₂×D₈	C₂³×C₄₁	1	2	yes	—
471	C₂×D₈	C₂³×C₄₁	1	2	yes	—
472	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
474	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
478	#127	—	2	2	no	—
479	#127	C₂³×C₄₁	1	2	yes	—
480	#126	—	2	4	no	—
481	#126	—	2	4	no	—
482	#126	—	2	4	no	—
483	#125	—	2	4	no	—
484	#125	C₂³×C₄₁	1	4	yes	—
485	#124	—	2	2	no	—
486	#124	—	2	2	no	—
487	#124	—	2	4	no	—
488	#124	—	2	2	no	—
489	#124	C₂³×C₄₁	1	4	yes	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	#123	—	2	4	no	—
493	C₂²⋊Q₈	—	2	4	no	—
494	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
495	#121	—	2	4	no	—
496	#121	—	2	4	no	—
497	#121	—	2	2	no	—
498	#121	—	2	4	no	—
499	#121	C₂³×C₄₁	1	4	yes	—
500	#121	C₂³×C₄₁	1	4	yes	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	2	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
506	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
507	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
508	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
509	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
510	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
511	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	D₄×C₄₁	1	2	yes	—
521	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
522	C₄×D₄	C₂³×C₄₁	1	4	yes	—
523	C₄×D₄	C₂³×C₄₁	1	4	yes	—
524	C₄×D₄	C₂³×C₄₁	1	2	yes	—
525	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
526	#117	—	2	4	no	—
527	#117	—	2	4	no	—
528	#117	D₄×C₄₁	1	1	yes	characteristic
529	#117	D₄×C₄₁	1	2	yes	—
530	#117	C₂³×C₄₁	1	4	yes	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
533	C₂×C₄²	—	2	2	no	—
534	C₂×C₄²	—	2	4	no	—
535	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
537	#107	C₂³×C₄₁	1	1	yes	characteristic
538	#107	C₂³×C₄₁	1	1	yes	characteristic
539	#107	C₂³×C₄₁	1	2	yes	—
540	#107	C₂³×C₄₁	1	2	yes	—
541	#107	C₂³×C₄₁	1	2	yes	—
542	#106	C₂³×C₄₁	1	4	yes	—
543	#106	C₂³×C₄₁	1	4	yes	—
544	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
545	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
546	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
547	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
548	#103	C₂³×C₄₁	1	2	yes	—
549	#103	C₂³×C₄₁	1	2	yes	—
550	#103	C₂³×C₄₁	1	2	yes	—
551	#103	C₂³×C₄₁	1	2	yes	—
552	#103	C₂³×C₄₁	1	4	yes	—
553	#103	C₂³×C₄₁	1	4	yes	—
554	#102	C₂³×C₄₁	1	4	yes	—
555	#102	C₂³×C₄₁	1	4	yes	—
556	#102	C₂³×C₄₁	1	4	yes	—
557	#102	C₂³×C₄₁	1	4	yes	—
558	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
560	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
561	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₄₁	1	2	yes	—
564	C₄×C₈	C₂³×C₄₁	1	2	yes	—
565	C₄×C₈	C₂³×C₄₁	1	2	yes	—
566	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
567	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
568	#41	—	2	4	no	—
569	#41	—	2	8	no	—
570	#41	—	4	4	no	—
571	#41	—	4	8	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	4	2	no	—
576	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
577	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
578	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
585	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
586	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
593	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
595	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
598	Q₁₆	—	2	4	no	—
599	Q₁₆	—	2	2	no	—
600	Q₁₆	#41×C₄₁	1	4	yes	complemented
601	SD₁₆	—	2	8	no	—
602	SD₁₆	—	4	4	no	—
603	D₈	—	2	4	no	—
604	D₈	—	4	2	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	4	no	—
607	C₂×C₈	—	4	1	no	—
608	C₂×C₈	—	4	2	no	—
609	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
611	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
612	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
613	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
614	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
626	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
627	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
628	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
641	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
642	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	C₂×D₄×C₄₁	1	2	yes	—
650	C₄²	C₂×D₄×C₄₁	1	2	yes	—
651	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
652	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
653	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
654	C₄²	C₂⁴×C₄₁	1	2	yes	—
655	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
656	C₂³	—	2	4	no	—
657	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
658	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	4	4	no	—
665	Q₈	C₂×#41×C₄₁	1	4	yes	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	4	no	—
670	D₄	—	4	8	no	—
671	D₄	—	4	8	no	—
672	D₄	—	4	4	no	—
673	D₄	—	8	2	no	—
674	D₄	—	8	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	8	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	2	no	—
692	C₂×C₄	#135×C₄₁	1	4	yes	complemented
693	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
694	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
701	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	1	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	1	no	—
706	C₈	—	2	2	no	—
707	C₈	C₂×#41×C₄₁	1	2	yes	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	4	no	—
716	C₂²	C₂×#135×C₄₁	1	2	yes	—
717	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	4	no	—
725	C₄	—	4	4	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	C₂×#135×C₄₁	1	2	yes	—
730	C₄	C₂×#135×C₄₁	1	2	yes	—
731	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
732	C₄	C₄₁×#585	1	1	yes	characteristic
733	C₂	—	2	2	no	—
734	C₂	—	4	2	no	—
735	C₂	—	8	4	no	—
736	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
737	C₂	C₂²×#135×C₄₁	1	1	yes	characteristic
738	C₂	C₄₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
socle	C₂²×C₄₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3480	C₂	semidirect
2. C₄₁×#3396	C₂	semidirect
3. C₄₁×#3383	C₂	semidirect
4. C₄₁×#3365	C₂	semidirect
5. C₄₁×#3342	C₂	semidirect
6. C₄₁×#3339	C₂	semidirect
7. C₄₁×#3304	C₂	semidirect
8. C₄₁×#3301	C₂	semidirect
9. C₄₁×#3287	C₂	semidirect
10. C₄₁×#3285	C₂	semidirect
11. C₄₁×#3169	C₂	semidirect
12. C₄₁×#3168	C₂	semidirect
13. C₄₁×#3103	C₂	semidirect
14. C₄₁×#3102	C₂	semidirect
15. C₈×#41×C₄₁	C₂	semidirect
16. C₄×#135×C₄₁	C₂	semidirect
17. C₂×C₄×Q₁₆×C₄₁	C₂	semidirect
230. Q₁₆×C₄₁	#41	semidirect
322. C₂×C₄×C₄₁	#135	semidirect
338. #61430	C₄₁	direct (N × H)
364. #3480	C₂×C₄₁	semidirect
365. #3396	C₂×C₄₁	semidirect
366. #3383	C₂×C₄₁	semidirect
367. #3365	C₂×C₄₁	semidirect
368. #3342	C₂×C₄₁	semidirect
369. #3339	C₂×C₄₁	semidirect
370. #3304	C₂×C₄₁	semidirect
371. #3301	C₂×C₄₁	semidirect
372. #3287	C₂×C₄₁	semidirect
373. #3285	C₂×C₄₁	semidirect
374. #3169	C₂×C₄₁	semidirect
375. #3168	C₂×C₄₁	semidirect
376. #3103	C₂×C₄₁	semidirect
377. #3102	C₂×C₄₁	semidirect
378. C₈×#41	C₂×C₄₁	semidirect
379. C₄×#135	C₂×C₄₁	semidirect
380. C₂×C₄×Q₁₆	C₂×C₄₁	semidirect
458. C₄₁	#61430	direct (N × H)
600. Q₁₆	#41×C₄₁	semidirect
692. C₂×C₄	#135×C₄₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3480	2
C₄₁×#3396	2
C₄₁×#3383	2
C₄₁×#3365	2
C₄₁×#3342	2
C₄₁×#3339	2
C₄₁×#3304	2
C₄₁×#3301	2
C₄₁×#3287	2
C₄₁×#3285	2
C₄₁×#3169	2
C₄₁×#3168	2
C₄₁×#3103	2
C₄₁×#3102	2
C₈×#41×C₄₁	2
C₄×#135×C₄₁	2
C₂×C₄×Q₁₆×C₄₁	2
#61430	41

Subgroups — C41×#61430 #23837631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61430 #23837631