Subgroups — C₄₁×#61910 #23838111

Order 10496.

1816 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3399	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3397	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3391	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3366	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3360	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3220	C₂	1	4	yes	maximal, complemented
10	C₄₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3119	C₂	1	4	yes	maximal, complemented
13	C₄₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#562	—	2	2	no	—
17	C₄₁×#559	C₂²	1	4	yes	—
18	C₄₁×#556	C₂²	1	2	yes	—
19	C₄₁×#555	—	2	1	no	—
20	C₄₁×#554	C₂²	1	2	yes	complemented
21	C₄₁×#554	C₂²	1	2	yes	complemented
22	C₄₁×#553	—	2	2	no	—
23	C₄₁×#550	C₂²	1	2	yes	—
24	C₄₁×#550	C₂²	1	2	yes	complemented
25	C₄₁×#550	C₂²	1	2	yes	complemented
26	C₄₁×#547	—	2	1	no	—
27	C₄₁×#547	—	2	1	no	—
28	C₄₁×#547	—	2	1	no	—
29	C₄₁×#540	C₂²	1	4	yes	—
30	C₄₁×#538	—	2	2	no	—
31	C₄₁×#537	—	2	2	no	—
32	C₄₁×#537	—	2	2	no	—
33	C₄₁×#535	C₂²	1	2	yes	—
34	C₄₁×#533	C₂²	1	1	yes	characteristic
35	C₄₁×#532	C₂²	1	1	yes	characteristic
36	C₄₁×#532	C₂²	1	1	yes	characteristic
37	C₄₁×#532	C₂²	1	1	yes	characteristic
38	C₄₁×#525	—	2	2	no	—
39	C₄₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#496	C₂²	1	4	yes	—
42	C₄₁×#496	C₂²	1	2	yes	complemented
43	C₄₁×#493	C₂²	1	4	yes	—
44	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#492	C₂²	1	1	yes	characteristic, complemented
46	C₄₁×#490	C₂²	1	4	yes	—
47	C₄₁×#489	C₂²	1	2	yes	complemented
48	C₄₁×#488	C₂²	1	4	yes	—
49	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
50	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₄₁×#481	C₂²	1	2	yes	—
52	C₄₁×#480	C₂²	1	2	yes	—
53	C₄₁×#479	C₂²	1	4	yes	complemented
54	C₄₁×#478	C₂²	1	4	yes	complemented
55	C₄₁×#476	C₂²	1	2	yes	—
56	C₄₁×#474	C₂²	1	2	yes	—
57	C₄₁×#463	C₂²	1	4	yes	—
58	C₄₁×#463	C₂²	1	4	yes	—
59	C₄₁×#463	C₂²	1	4	yes	complemented
60	C₄₁×#461	C₂²	1	2	yes	complemented
61	C₄₁×#460	C₂²	1	4	yes	complemented
62	C₄₁×#459	C₂²	1	2	yes	—
63	C₄₁×#459	C₂²	1	2	yes	—
64	C₄₁×#459	C₂²	1	4	yes	—
65	C₄₁×#459	C₂²	1	4	yes	—
66	C₄₁×#459	C₂²	1	2	yes	complemented
67	C₄₁×#459	C₂²	1	4	yes	complemented
68	C₄₁×#449	C₂²	1	4	yes	—
69	C₄₁×#449	C₂²	1	4	yes	—
70	C₄₁×#447	C₂²	1	2	yes	—
71	C₄₁×#447	C₂²	1	2	yes	—
72	C₄₁×#446	C₂²	1	2	yes	complemented
73	C₄₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₄₁	C₂²	1	2	yes	complemented
75	C₄₁×#442	C₂²	1	4	yes	—
76	C₄₁×#442	C₂²	1	4	yes	complemented
77	C₄₁×#440	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
79	C₄×D₈×C₄₁	C₂²	1	2	yes	—
80	C₄×D₈×C₄₁	C₂²	1	2	yes	—
81	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
82	C₄₁×#433	C₂²	1	4	yes	—
83	C₄₁×#432	C₂²	1	1	yes	characteristic
84	C₄₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₄₁	—	2	2	no	—
86	C₂×#41×C₄₁	—	2	2	no	—
87	C₂×#41×C₄₁	—	2	2	no	—
88	C₂×#41×C₄₁	—	2	1	no	—
89	C₂×#41×C₄₁	—	2	1	no	—
90	C₂×#41×C₄₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₁	—	2	1	no	—
93	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
95	C₂×D₈×C₄₁	C₂³	1	2	yes	—
96	C₂×D₈×C₄₁	C₂³	1	2	yes	—
97	C₂×D₈×C₄₁	C₂³	1	4	yes	—
98	C₂×D₈×C₄₁	C₂³	1	4	yes	—
99	C₂×D₈×C₄₁	C₂³	1	4	yes	—
100	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
101	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
105	#127×C₄₁	C₂³	1	1	yes	characteristic
106	#127×C₄₁	C₂³	1	1	yes	characteristic
107	#127×C₄₁	C₂³	1	1	yes	characteristic
108	#127×C₄₁	C₂³	1	4	yes	—
109	#127×C₄₁	C₂³	1	4	yes	—
110	#126×C₄₁	—	2	4	no	—
111	#125×C₄₁	D₄	1	2	yes	—
112	#125×C₄₁	C₂³	1	4	yes	—
113	#124×C₄₁	—	2	4	no	—
114	#124×C₄₁	—	2	1	no	—
115	#124×C₄₁	—	2	1	no	—
116	#124×C₄₁	C₂³	1	2	yes	—
117	#124×C₄₁	C₂³	1	4	yes	—
118	#123×C₄₁	—	2	4	no	—
119	#123×C₄₁	—	2	4	no	—
120	#123×C₄₁	—	2	4	no	—
121	#123×C₄₁	—	2	4	no	—
122	C₂²⋊Q₈×C₄₁	—	2	2	no	—
123	C₂²⋊Q₈×C₄₁	—	2	2	no	—
124	C₂²⋊Q₈×C₄₁	—	2	2	no	—
125	C₂²⋊Q₈×C₄₁	—	2	4	no	—
126	C₂²⋊Q₈×C₄₁	—	2	4	no	—
127	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
128	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
129	#121×C₄₁	—	2	1	no	—
130	#121×C₄₁	—	2	1	no	—
131	#121×C₄₁	—	2	1	no	—
132	#121×C₄₁	—	2	1	no	—
133	#121×C₄₁	—	2	2	no	—
134	#121×C₄₁	—	2	2	no	—
135	#121×C₄₁	—	2	2	no	—
136	#121×C₄₁	—	2	2	no	—
137	#121×C₄₁	—	2	2	no	—
138	#121×C₄₁	—	2	4	no	—
139	#121×C₄₁	—	2	4	no	—
140	#121×C₄₁	—	2	4	no	—
141	#121×C₄₁	—	2	4	no	—
142	#121×C₄₁	—	2	4	no	—
143	#121×C₄₁	C₂³	1	2	yes	—
144	#121×C₄₁	C₂³	1	2	yes	—
145	#120×C₄₁	—	2	4	no	—
146	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
147	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
149	C₄×D₄×C₄₁	—	2	4	no	—
150	C₄×D₄×C₄₁	—	2	4	no	—
151	C₄×D₄×C₄₁	—	2	1	no	—
152	C₄×D₄×C₄₁	—	2	1	no	—
153	C₄×D₄×C₄₁	—	2	1	no	—
154	C₄×D₄×C₄₁	—	2	1	no	—
155	C₄×D₄×C₄₁	—	2	1	no	—
156	C₄×D₄×C₄₁	—	2	1	no	—
157	C₄×D₄×C₄₁	C₂³	1	2	yes	—
158	C₄×D₄×C₄₁	C₂³	1	2	yes	—
159	C₄×D₄×C₄₁	C₂³	1	4	yes	—
160	C₄×D₄×C₄₁	C₂³	1	2	yes	—
161	C₄×D₄×C₄₁	C₂³	1	2	yes	—
162	C₄×D₄×C₄₁	C₂³	1	4	yes	—
163	C₄×D₄×C₄₁	C₂³	1	4	yes	—
164	#117×C₄₁	—	2	2	no	—
165	#117×C₄₁	—	2	2	no	—
166	#117×C₄₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
168	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
169	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
172	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
173	#107×C₄₁	C₂³	1	2	yes	—
174	#107×C₄₁	C₂³	1	2	yes	—
175	#106×C₄₁	C₂³	1	4	yes	—
176	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
179	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
180	#103×C₄₁	C₂³	1	4	yes	—
181	#103×C₄₁	C₂³	1	4	yes	—
182	#102×C₄₁	C₂³	1	2	yes	—
183	#102×C₄₁	C₂³	1	2	yes	—
184	#102×C₄₁	C₂³	1	2	yes	—
185	#102×C₄₁	C₂³	1	2	yes	—
186	#102×C₄₁	C₂³	1	4	yes	—
187	#102×C₄₁	C₂³	1	4	yes	—
188	#102×C₄₁	C₂³	1	4	yes	—
189	#102×C₄₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
192	#97×C₄₁	C₂³	1	2	yes	—
193	#97×C₄₁	C₂³	1	4	yes	—
194	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₁	C₂³	1	4	yes	—
197	C₂⁴×C₄₁	—	2	1	no	—
198	#41×C₄₁	—	4	4	no	—
199	#41×C₄₁	—	8	2	no	—
200	#41×C₄₁	—	8	2	no	—
201	#41×C₄₁	—	8	4	no	—
202	#41×C₄₁	—	8	4	no	—
203	#41×C₄₁	—	8	4	no	—
204	C₂×Q₈×C₄₁	—	2	1	no	—
205	C₂×Q₈×C₄₁	—	2	1	no	—
206	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₄₁	—	2	2	no	—
210	C₂×D₄×C₄₁	—	2	2	no	—
211	C₂×D₄×C₄₁	—	2	2	no	—
212	C₂×D₄×C₄₁	—	2	1	no	—
213	C₂×D₄×C₄₁	—	2	1	no	—
214	C₂×D₄×C₄₁	—	2	1	no	—
215	C₂×D₄×C₄₁	—	2	1	no	—
216	C₂×D₄×C₄₁	—	2	4	no	—
217	C₂×D₄×C₄₁	—	2	1	no	—
218	C₂×D₄×C₄₁	—	2	4	no	—
219	C₂×D₄×C₄₁	—	2	4	no	—
220	C₂×D₄×C₄₁	—	2	4	no	—
221	C₂×D₄×C₄₁	—	2	1	no	—
222	C₂×D₄×C₄₁	—	2	1	no	—
223	C₂×D₄×C₄₁	—	4	2	no	—
224	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
225	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
227	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₄₁	—	2	1	no	—
229	C₂²×C₄×C₄₁	—	2	2	no	—
230	C₂²×C₄×C₄₁	—	2	2	no	—
231	C₂²×C₄×C₄₁	—	2	2	no	—
232	C₂²×C₄×C₄₁	—	2	2	no	—
233	C₂²×C₄×C₄₁	—	2	4	no	—
234	C₂²×C₄×C₄₁	—	2	4	no	—
235	C₂²×C₄×C₄₁	—	2	4	no	—
236	C₂²×C₄×C₄₁	—	2	2	no	—
237	C₂²×C₄×C₄₁	—	8	2	no	—
238	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
241	SD₁₆×C₄₁	—	4	4	no	—
242	SD₁₆×C₄₁	—	4	4	no	—
243	D₈×C₄₁	—	4	4	no	—
244	D₈×C₄₁	—	4	2	no	—
245	D₈×C₄₁	—	4	4	no	—
246	D₈×C₄₁	—	4	4	no	—
247	D₈×C₄₁	—	4	2	no	—
248	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
250	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
251	C₄⋊C₄×C₄₁	—	2	1	no	—
252	C₄⋊C₄×C₄₁	—	2	1	no	—
253	C₄⋊C₄×C₄₁	—	2	1	no	—
254	C₄⋊C₄×C₄₁	—	2	4	no	—
255	C₄⋊C₄×C₄₁	—	2	4	no	—
256	C₄⋊C₄×C₄₁	—	2	4	no	—
257	C₄⋊C₄×C₄₁	—	2	1	no	—
258	C₄⋊C₄×C₄₁	—	2	1	no	—
259	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
265	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
268	C₂²⋊C₄×C₄₁	—	2	2	no	—
269	C₂²⋊C₄×C₄₁	—	2	2	no	—
270	C₂²⋊C₄×C₄₁	—	2	4	no	—
271	C₂²⋊C₄×C₄₁	—	2	4	no	—
272	C₂²⋊C₄×C₄₁	—	2	2	no	—
273	C₂²⋊C₄×C₄₁	—	2	4	no	—
274	C₂²⋊C₄×C₄₁	—	2	2	no	—
275	C₂²⋊C₄×C₄₁	—	2	2	no	—
276	C₂²⋊C₄×C₄₁	—	2	2	no	—
277	C₂²⋊C₄×C₄₁	—	2	4	no	—
278	C₂²⋊C₄×C₄₁	—	2	4	no	—
279	C₂²⋊C₄×C₄₁	—	2	2	no	—
280	C₂²⋊C₄×C₄₁	—	2	2	no	—
281	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
282	C₄²×C₄₁	—	2	4	no	—
283	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
286	C₄²×C₄₁	C₂⁴	1	4	yes	—
287	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
288	C₂³×C₄₁	—	2	2	no	—
289	C₂³×C₄₁	—	2	2	no	—
290	C₂³×C₄₁	—	2	2	no	—
291	C₂³×C₄₁	—	2	2	no	—
292	C₂³×C₄₁	—	4	2	no	—
293	C₂³×C₄₁	—	8	1	no	—
294	C₂³×C₄₁	—	8	1	no	—
295	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₄₁	—	2	4	no	—
297	Q₈×C₄₁	—	2	4	no	—
298	Q₈×C₄₁	—	4	2	no	—
299	Q₈×C₄₁	—	8	1	no	—
300	Q₈×C₄₁	—	8	1	no	—
301	D₄×C₄₁	—	2	2	no	—
302	D₄×C₄₁	—	2	4	no	—
303	D₄×C₄₁	—	2	2	no	—
304	D₄×C₄₁	—	2	2	no	—
305	D₄×C₄₁	—	2	4	no	—
306	D₄×C₄₁	—	2	2	no	—
307	D₄×C₄₁	—	4	2	no	—
308	D₄×C₄₁	—	4	2	no	—
309	D₄×C₄₁	—	4	4	no	—
310	D₄×C₄₁	—	4	2	no	—
311	D₄×C₄₁	—	4	2	no	—
312	D₄×C₄₁	—	8	1	no	—
313	D₄×C₄₁	—	8	4	no	—
314	D₄×C₄₁	—	8	1	no	—
315	D₄×C₄₁	—	8	4	no	—
316	D₄×C₄₁	—	8	1	no	—
317	D₄×C₄₁	—	8	4	no	—
318	D₄×C₄₁	—	8	4	no	—
319	D₄×C₄₁	—	8	2	no	—
320	D₄×C₄₁	—	8	2	no	—
321	C₂×C₄×C₄₁	—	2	2	no	—
322	C₂×C₄×C₄₁	—	2	2	no	—
323	C₂×C₄×C₄₁	—	2	2	no	—
324	C₂×C₄×C₄₁	—	2	2	no	—
325	C₂×C₄×C₄₁	—	2	2	no	—
326	C₂×C₄×C₄₁	—	2	2	no	—
327	C₂×C₄×C₄₁	—	4	1	no	—
328	C₂×C₄×C₄₁	—	4	4	no	—
329	C₂×C₄×C₄₁	—	4	4	no	—
330	C₂×C₄×C₄₁	—	4	4	no	—
331	C₂×C₄×C₄₁	—	4	4	no	—
332	C₂×C₄×C₄₁	—	8	2	no	—
333	C₂×C₄×C₄₁	—	8	4	no	—
334	C₂×C₄×C₄₁	—	8	4	no	—
335	C₂×C₄×C₄₁	—	8	4	no	—
336	C₂×C₄×C₄₁	—	8	1	no	—
337	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
343	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
345	C₈×C₄₁	—	2	2	no	—
346	C₈×C₄₁	—	2	4	no	—
347	C₈×C₄₁	—	2	2	no	—
348	#61910	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₂²×C₄₁	—	2	1	no	—
350	C₂²×C₄₁	—	2	1	no	—
351	C₂²×C₄₁	—	2	1	no	—
352	C₂²×C₄₁	—	4	2	no	—
353	C₂²×C₄₁	—	4	2	no	—
354	C₂²×C₄₁	—	4	2	no	—
355	C₂²×C₄₁	—	4	2	no	—
356	C₂²×C₄₁	—	4	2	no	—
357	C₂²×C₄₁	—	4	2	no	—
358	C₂²×C₄₁	—	4	2	no	—
359	C₂²×C₄₁	—	4	2	no	—
360	C₂²×C₄₁	—	4	2	no	—
361	C₂²×C₄₁	—	4	2	no	—
362	C₂²×C₄₁	—	4	2	no	—
363	C₂²×C₄₁	—	4	2	no	—
364	C₂²×C₄₁	—	8	4	no	—
365	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₄₁	—	2	1	no	—
367	C₄×C₄₁	—	2	1	no	—
368	C₄×C₄₁	—	2	4	no	—
369	C₄×C₄₁	—	2	1	no	—
370	C₄×C₄₁	—	2	1	no	—
371	C₄×C₄₁	—	2	4	no	—
372	C₄×C₄₁	—	4	2	no	—
373	C₄×C₄₁	—	4	2	no	—
374	C₄×C₄₁	—	4	2	no	—
375	C₄×C₄₁	—	4	2	no	—
376	C₄×C₄₁	#576	1	2	yes	—
377	C₄×C₄₁	#585	1	2	yes	—
378	#3548	C₂×C₄₁	1	1	yes	characteristic, complemented
379	#3506	C₂×C₄₁	1	1	yes	characteristic, complemented
380	#3399	C₂×C₄₁	1	4	yes	complemented
381	#3397	C₂×C₄₁	1	2	yes	complemented
382	#3391	C₂×C₄₁	1	2	yes	complemented
383	#3370	C₂×C₄₁	1	4	yes	complemented
384	#3366	C₂×C₄₁	1	2	yes	complemented
385	#3360	C₂×C₄₁	1	2	yes	complemented
386	#3220	C₂×C₄₁	1	4	yes	complemented
387	#3214	C₂×C₄₁	1	1	yes	characteristic, complemented
388	#3207	C₂×C₄₁	1	1	yes	characteristic, complemented
389	#3119	C₂×C₄₁	1	4	yes	complemented
390	#3109	C₂×C₄₁	1	1	yes	characteristic, complemented
391	#3100	C₂×C₄₁	1	1	yes	characteristic, complemented
392	#2985	C₂×C₄₁	1	1	yes	characteristic, complemented
393	C₂×C₄₁	—	4	1	no	—
394	C₂×C₄₁	—	8	2	no	—
395	C₂×C₄₁	—	8	2	no	—
396	C₂×C₄₁	—	8	2	no	—
397	C₂×C₄₁	—	8	2	no	—
398	C₂×C₄₁	#3487	1	1	yes	characteristic
399	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
400	C₂×C₄₁	#3585	1	1	yes	characteristic
401	#562	—	2	2	no	—
402	#559	C₂²×C₄₁	1	4	yes	—
403	#556	C₂²×C₄₁	1	2	yes	—
404	#555	—	2	1	no	—
405	#554	C₂²×C₄₁	1	2	yes	complemented
406	#554	C₂²×C₄₁	1	2	yes	complemented
407	#553	—	2	2	no	—
408	#550	C₂²×C₄₁	1	2	yes	—
409	#550	C₂²×C₄₁	1	2	yes	complemented
410	#550	C₂²×C₄₁	1	2	yes	complemented
411	#547	—	2	1	no	—
412	#547	—	2	1	no	—
413	#547	—	2	1	no	—
414	#540	C₂²×C₄₁	1	4	yes	—
415	#538	—	2	2	no	—
416	#537	—	2	2	no	—
417	#537	—	2	2	no	—
418	#535	C₂²×C₄₁	1	2	yes	—
419	#533	C₂²×C₄₁	1	1	yes	characteristic
420	#532	C₂²×C₄₁	1	1	yes	characteristic
421	#532	C₂²×C₄₁	1	1	yes	characteristic
422	#532	C₂²×C₄₁	1	1	yes	characteristic
423	#525	—	2	2	no	—
424	#520	C₂²×C₄₁	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
426	#496	C₂²×C₄₁	1	4	yes	—
427	#496	C₂²×C₄₁	1	2	yes	complemented
428	#493	C₂²×C₄₁	1	4	yes	—
429	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
430	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
431	#490	C₂²×C₄₁	1	4	yes	—
432	#489	C₂²×C₄₁	1	2	yes	complemented
433	#488	C₂²×C₄₁	1	4	yes	—
434	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
435	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
436	#481	C₂²×C₄₁	1	2	yes	—
437	#480	C₂²×C₄₁	1	2	yes	—
438	#479	C₂²×C₄₁	1	4	yes	complemented
439	#478	C₂²×C₄₁	1	4	yes	complemented
440	#476	C₂²×C₄₁	1	2	yes	—
441	#474	C₂²×C₄₁	1	2	yes	—
442	#463	C₂²×C₄₁	1	4	yes	—
443	#463	C₂²×C₄₁	1	4	yes	—
444	#463	C₂²×C₄₁	1	4	yes	complemented
445	#461	C₂²×C₄₁	1	2	yes	complemented
446	#460	C₂²×C₄₁	1	4	yes	complemented
447	#459	C₂²×C₄₁	1	2	yes	—
448	#459	C₂²×C₄₁	1	2	yes	—
449	#459	C₂²×C₄₁	1	4	yes	—
450	#459	C₂²×C₄₁	1	4	yes	—
451	#459	C₂²×C₄₁	1	2	yes	complemented
452	#459	C₂²×C₄₁	1	4	yes	complemented
453	#449	C₂²×C₄₁	1	4	yes	—
454	#449	C₂²×C₄₁	1	4	yes	—
455	#447	C₂²×C₄₁	1	2	yes	—
456	#447	C₂²×C₄₁	1	2	yes	—
457	#446	C₂²×C₄₁	1	2	yes	complemented
458	#446	C₂²×C₄₁	1	4	yes	complemented
459	C₈×Q₈	C₂²×C₄₁	1	2	yes	complemented
460	#442	C₂²×C₄₁	1	4	yes	—
461	#442	C₂²×C₄₁	1	4	yes	complemented
462	#440	C₂²×C₄₁	1	4	yes	complemented
463	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
464	C₄×D₈	C₂²×C₄₁	1	2	yes	—
465	C₄×D₈	C₂²×C₄₁	1	2	yes	—
466	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
467	#433	C₂²×C₄₁	1	4	yes	—
468	#432	C₂²×C₄₁	1	1	yes	characteristic
469	#431	C₂²×C₄₁	1	1	yes	characteristic
470	C₄₁	#61910	1	1	yes	characteristic, direct product factor, Sylow
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	—	2	2	no	—
474	C₂×#41	—	2	1	no	—
475	C₂×#41	—	2	1	no	—
476	C₂×#41	C₂³×C₄₁	1	2	yes	—
477	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
480	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
481	C₂×D₈	C₂³×C₄₁	1	2	yes	—
482	C₂×D₈	C₂³×C₄₁	1	2	yes	—
483	C₂×D₈	C₂³×C₄₁	1	4	yes	—
484	C₂×D₈	C₂³×C₄₁	1	4	yes	—
485	C₂×D₈	C₂³×C₄₁	1	4	yes	—
486	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
487	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
491	#127	C₂³×C₄₁	1	1	yes	characteristic
492	#127	C₂³×C₄₁	1	1	yes	characteristic
493	#127	C₂³×C₄₁	1	1	yes	characteristic
494	#127	C₂³×C₄₁	1	4	yes	—
495	#127	C₂³×C₄₁	1	4	yes	—
496	#126	—	2	4	no	—
497	#125	D₄×C₄₁	1	2	yes	—
498	#125	C₂³×C₄₁	1	4	yes	—
499	#124	—	2	4	no	—
500	#124	—	2	1	no	—
501	#124	—	2	1	no	—
502	#124	C₂³×C₄₁	1	2	yes	—
503	#124	C₂³×C₄₁	1	4	yes	—
504	#123	—	2	4	no	—
505	#123	—	2	4	no	—
506	#123	—	2	4	no	—
507	#123	—	2	4	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	2	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
514	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
515	#121	—	2	1	no	—
516	#121	—	2	1	no	—
517	#121	—	2	1	no	—
518	#121	—	2	1	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	—	2	4	no	—
525	#121	—	2	4	no	—
526	#121	—	2	4	no	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#121	C₂³×C₄₁	1	2	yes	—
530	#121	C₂³×C₄₁	1	2	yes	—
531	#120	—	2	4	no	—
532	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
533	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
534	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	C₂³×C₄₁	1	2	yes	—
544	C₄×D₄	C₂³×C₄₁	1	2	yes	—
545	C₄×D₄	C₂³×C₄₁	1	4	yes	—
546	C₄×D₄	C₂³×C₄₁	1	2	yes	—
547	C₄×D₄	C₂³×C₄₁	1	2	yes	—
548	C₄×D₄	C₂³×C₄₁	1	4	yes	—
549	C₄×D₄	C₂³×C₄₁	1	4	yes	—
550	#117	—	2	2	no	—
551	#117	—	2	2	no	—
552	#117	C₂³×C₄₁	1	2	yes	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
559	#107	C₂³×C₄₁	1	2	yes	—
560	#107	C₂³×C₄₁	1	2	yes	—
561	#106	C₂³×C₄₁	1	4	yes	—
562	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
563	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
564	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
565	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
566	#103	C₂³×C₄₁	1	4	yes	—
567	#103	C₂³×C₄₁	1	4	yes	—
568	#102	C₂³×C₄₁	1	2	yes	—
569	#102	C₂³×C₄₁	1	2	yes	—
570	#102	C₂³×C₄₁	1	2	yes	—
571	#102	C₂³×C₄₁	1	2	yes	—
572	#102	C₂³×C₄₁	1	4	yes	—
573	#102	C₂³×C₄₁	1	4	yes	—
574	#102	C₂³×C₄₁	1	4	yes	—
575	#102	C₂³×C₄₁	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
578	#97	C₂³×C₄₁	1	2	yes	—
579	#97	C₂³×C₄₁	1	4	yes	—
580	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
581	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
582	C₄×C₈	C₂³×C₄₁	1	4	yes	—
583	C₂⁴	—	2	1	no	—
584	#41	—	4	4	no	—
585	#41	—	8	2	no	—
586	#41	—	8	2	no	—
587	#41	—	8	4	no	—
588	#41	—	8	4	no	—
589	#41	—	8	4	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
593	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
594	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
611	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
612	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
613	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	8	2	no	—
624	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
627	SD₁₆	—	4	4	no	—
628	SD₁₆	—	4	4	no	—
629	D₈	—	4	4	no	—
630	D₈	—	4	2	no	—
631	D₈	—	4	4	no	—
632	D₈	—	4	4	no	—
633	D₈	—	4	2	no	—
634	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
635	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
636	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
646	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
647	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
648	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
650	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
651	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
668	C₄²	—	2	4	no	—
669	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
670	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
671	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
672	C₄²	C₂⁴×C₄₁	1	4	yes	—
673	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	8	1	no	—
680	C₂³	—	8	1	no	—
681	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
682	Q₈	—	2	4	no	—
683	Q₈	—	2	4	no	—
684	Q₈	—	4	2	no	—
685	Q₈	—	8	1	no	—
686	Q₈	—	8	1	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	2	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	2	no	—
698	D₄	—	8	1	no	—
699	D₄	—	8	4	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	1	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	1	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	1	no	—
723	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
724	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
729	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
730	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	2	4	no	—
733	C₈	—	2	2	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	8	4	no	—
750	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	4	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	C₄₁×#576	1	2	yes	—
762	C₄	C₄₁×#585	1	2	yes	—
763	C₂	—	4	1	no	—
764	C₂	—	8	2	no	—
765	C₂	—	8	2	no	—
766	C₂	—	8	2	no	—
767	C₂	—	8	2	no	—
768	C₂	C₄₁×#3487	1	1	yes	characteristic
769	C₂	C₂×C₄₁×#576	1	1	yes	characteristic
770	C₂	C₄₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3548	C₂	semidirect
2. C₄₁×#3506	C₂	semidirect
3. C₄₁×#3399	C₂	semidirect
4. C₄₁×#3397	C₂	semidirect
5. C₄₁×#3391	C₂	semidirect
6. C₄₁×#3370	C₂	semidirect
7. C₄₁×#3366	C₂	semidirect
8. C₄₁×#3360	C₂	semidirect
9. C₄₁×#3220	C₂	semidirect
10. C₄₁×#3214	C₂	semidirect
11. C₄₁×#3207	C₂	semidirect
12. C₄₁×#3119	C₂	semidirect
13. C₄₁×#3109	C₂	semidirect
14. C₄₁×#3100	C₂	semidirect
15. C₄₁×#2985	C₂	semidirect
20. C₄₁×#554	C₂²	semidirect
21. C₄₁×#554	C₂²	semidirect
24. C₄₁×#550	C₂²	semidirect
25. C₄₁×#550	C₂²	semidirect
42. C₄₁×#496	C₂²	semidirect
44. C₄₁×#493	C₂²	semidirect
45. C₄₁×#492	C₂²	semidirect
47. C₄₁×#489	C₂²	semidirect
49. C₄₁×#487	C₂²	semidirect
50. C₄₁×#486	C₂²	semidirect
53. C₄₁×#479	C₂²	semidirect
54. C₄₁×#478	C₂²	semidirect
59. C₄₁×#463	C₂²	semidirect
60. C₄₁×#461	C₂²	semidirect
61. C₄₁×#460	C₂²	semidirect
66. C₄₁×#459	C₂²	semidirect
67. C₄₁×#459	C₂²	semidirect
72. C₄₁×#446	C₂²	semidirect
73. C₄₁×#446	C₂²	semidirect
74. C₈×Q₈×C₄₁	C₂²	semidirect
76. C₄₁×#442	C₂²	semidirect
77. C₄₁×#440	C₂²	semidirect
78. C₄×SD₁₆×C₄₁	C₂²	semidirect
81. C₄×D₈×C₄₁	C₂²	semidirect
348. #61910	C₄₁	direct (N × H)
378. #3548	C₂×C₄₁	semidirect
379. #3506	C₂×C₄₁	semidirect
380. #3399	C₂×C₄₁	semidirect
381. #3397	C₂×C₄₁	semidirect
382. #3391	C₂×C₄₁	semidirect
383. #3370	C₂×C₄₁	semidirect
384. #3366	C₂×C₄₁	semidirect
385. #3360	C₂×C₄₁	semidirect
386. #3220	C₂×C₄₁	semidirect
387. #3214	C₂×C₄₁	semidirect
388. #3207	C₂×C₄₁	semidirect
389. #3119	C₂×C₄₁	semidirect
390. #3109	C₂×C₄₁	semidirect
391. #3100	C₂×C₄₁	semidirect
392. #2985	C₂×C₄₁	semidirect
405. #554	C₂²×C₄₁	semidirect
406. #554	C₂²×C₄₁	semidirect
409. #550	C₂²×C₄₁	semidirect
410. #550	C₂²×C₄₁	semidirect
427. #496	C₂²×C₄₁	semidirect
429. #493	C₂²×C₄₁	semidirect
430. #492	C₂²×C₄₁	semidirect
432. #489	C₂²×C₄₁	semidirect
434. #487	C₂²×C₄₁	semidirect
435. #486	C₂²×C₄₁	semidirect
438. #479	C₂²×C₄₁	semidirect
439. #478	C₂²×C₄₁	semidirect
444. #463	C₂²×C₄₁	semidirect
445. #461	C₂²×C₄₁	semidirect
446. #460	C₂²×C₄₁	semidirect
451. #459	C₂²×C₄₁	semidirect
452. #459	C₂²×C₄₁	semidirect
457. #446	C₂²×C₄₁	semidirect
458. #446	C₂²×C₄₁	semidirect
459. C₈×Q₈	C₂²×C₄₁	semidirect
461. #442	C₂²×C₄₁	semidirect
462. #440	C₂²×C₄₁	semidirect
463. C₄×SD₁₆	C₂²×C₄₁	semidirect
466. C₄×D₈	C₂²×C₄₁	semidirect
470. C₄₁	#61910	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3548	2
C₄₁×#3506	2
C₄₁×#3399	2
C₄₁×#3397	2
C₄₁×#3391	2
C₄₁×#3370	2
C₄₁×#3366	2
C₄₁×#3360	2
C₄₁×#3220	2
C₄₁×#3214	2
C₄₁×#3207	2
C₄₁×#3119	2
C₄₁×#3109	2
C₄₁×#3100	2
C₄₁×#2985	2
#61910	41

Subgroups — C41×#61910 #23838111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61910 #23838111