Subgroups — C₄₁×#17559 #23793760

Order 10496.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 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	1	yes	maximal, characteristic
2	C₂×C₄₁×#407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1513	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1511	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1510	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1501	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₁	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₁	—	2	1	no	—
11	C₄₁×#525	—	2	1	no	—
12	C₄₁×#525	—	2	1	no	—
13	C₄₁×#525	—	2	1	no	—
14	C₄₁×#525	—	2	1	no	—
15	C₄₁×#525	C₄	1	2	yes	complemented
16	C₄₁×#525	C₄	1	2	yes	complemented
17	C₄₁×#525	C₂²	1	2	yes	—
18	C₄₁×#525	C₂²	1	2	yes	—
19	C₂×#123×C₄₁	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
21	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#121×C₄₁	C₄	1	1	yes	characteristic, complemented
23	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#120×C₄₁	—	2	1	no	—
25	C₂×C₄×D₄×C₄₁	—	2	1	no	—
26	C₂×C₄×D₄×C₄₁	—	2	1	no	—
27	C₂×#117×C₄₁	—	2	1	no	—
28	C₂×#117×C₄₁	C₄	1	1	yes	characteristic, complemented
29	C₄₁×#407	—	2	1	no	—
30	C₄₁×#407	—	2	1	no	—
31	C₄₁×#407	C₂²	1	2	yes	—
32	C₄₁×#407	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
34	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
35	C₄₁×#381	C₂²	1	2	yes	—
36	C₄₁×#380	—	2	1	no	—
37	C₄₁×#380	C₂²	1	2	yes	complemented
38	C₄₁×#379	—	2	1	no	—
39	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
40	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	complemented
41	C₄₁×#328	C₂²	1	8	yes	complemented
42	C₄₁×#327	C₂²	1	8	yes	complemented
43	C₂⁵×C₄₁	D₄	1	1	yes	characteristic
44	C₂×#41×C₄₁	—	2	1	no	—
45	C₂×#41×C₄₁	—	2	1	no	—
46	C₂×#41×C₄₁	—	4	4	no	—
47	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
48	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
49	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	1	no	—
52	C₂²×D₄×C₄₁	—	2	1	no	—
53	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₁	—	2	1	no	—
55	C₂³×C₄×C₄₁	—	4	4	no	—
56	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₄₁	—	2	2	no	—
71	C₂×M₁₆×C₄₁	—	2	2	no	—
72	C₂×M₁₆×C₄₁	—	4	4	no	—
73	C₂²×C₈×C₄₁	—	2	2	no	—
74	#123×C₄₁	—	2	2	no	—
75	#123×C₄₁	—	2	2	no	—
76	#123×C₄₁	—	2	2	no	—
77	#123×C₄₁	—	2	2	no	—
78	C₂²⋊Q₈×C₄₁	—	2	1	no	—
79	C₂²⋊Q₈×C₄₁	—	2	1	no	—
80	C₂²⋊Q₈×C₄₁	—	2	1	no	—
81	C₂²⋊Q₈×C₄₁	—	2	1	no	—
82	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
83	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
84	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
85	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
86	#121×C₄₁	—	2	1	no	—
87	#121×C₄₁	—	2	1	no	—
88	#121×C₄₁	—	2	1	no	—
89	#121×C₄₁	—	2	1	no	—
90	#121×C₄₁	C₂×C₄	1	2	yes	—
91	#121×C₄₁	C₂×C₄	1	2	yes	—
92	#121×C₄₁	C₂×C₄	1	2	yes	—
93	#121×C₄₁	C₂³	1	2	yes	—
94	#120×C₄₁	—	2	2	no	—
95	#120×C₄₁	—	2	2	no	—
96	#120×C₄₁	—	2	2	no	—
97	#120×C₄₁	—	2	2	no	—
98	C₄×D₄×C₄₁	—	2	2	no	—
99	C₄×D₄×C₄₁	—	2	2	no	—
100	C₄×D₄×C₄₁	—	2	2	no	—
101	C₄×D₄×C₄₁	—	2	2	no	—
102	C₄×D₄×C₄₁	—	2	2	no	—
103	C₄×D₄×C₄₁	—	2	2	no	—
104	C₄×D₄×C₄₁	—	2	2	no	—
105	C₄×D₄×C₄₁	—	2	2	no	—
106	#117×C₄₁	—	2	1	no	—
107	#117×C₄₁	—	2	1	no	—
108	#117×C₄₁	—	4	4	no	—
109	#117×C₄₁	C₂×C₄	1	2	yes	—
110	#117×C₄₁	C₂×C₄	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
112	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
122	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
124	C₂×C₄²×C₄₁	—	2	1	no	—
125	C₂×C₄²×C₄₁	—	2	2	no	—
126	C₂²⋊C₈×C₄₁	—	2	2	no	—
127	C₂²⋊C₈×C₄₁	—	2	2	no	—
128	C₂²⋊C₈×C₄₁	—	2	2	no	—
129	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
130	#95×C₄₁	—	2	2	no	—
131	#95×C₄₁	C₂³	1	4	yes	—
132	C₂⁴×C₄₁	—	2	1	no	—
133	C₂⁴×C₄₁	—	4	2	no	—
134	C₂⁴×C₄₁	—	4	2	no	—
135	C₂⁴×C₄₁	—	4	2	no	—
136	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
137	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
138	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
139	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
140	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
143	#41×C₄₁	—	4	4	no	—
144	#41×C₄₁	—	4	4	no	—
145	#41×C₄₁	—	4	4	no	—
146	#41×C₄₁	—	4	4	no	—
147	C₂×Q₈×C₄₁	—	2	1	no	—
148	C₂×Q₈×C₄₁	—	4	2	no	—
149	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₄₁	—	2	2	no	—
151	C₂×D₄×C₄₁	—	2	2	no	—
152	C₂×D₄×C₄₁	—	2	2	no	—
153	C₂×D₄×C₄₁	—	2	2	no	—
154	C₂×D₄×C₄₁	—	2	2	no	—
155	C₂×D₄×C₄₁	—	2	2	no	—
156	C₂×D₄×C₄₁	—	2	1	no	—
157	C₂×D₄×C₄₁	—	4	2	no	—
158	C₂×D₄×C₄₁	—	4	4	no	—
159	C₂×D₄×C₄₁	—	4	4	no	—
160	C₂×D₄×C₄₁	—	4	4	no	—
161	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₄₁	—	2	4	no	—
163	C₂²×C₄×C₄₁	—	2	4	no	—
164	C₂²×C₄×C₄₁	—	2	4	no	—
165	C₂²×C₄×C₄₁	—	2	1	no	—
166	C₂²×C₄×C₄₁	—	2	1	no	—
167	C₂²×C₄×C₄₁	—	2	1	no	—
168	C₂²×C₄×C₄₁	—	2	2	no	—
169	C₂²×C₄×C₄₁	—	2	2	no	—
170	C₂²×C₄×C₄₁	—	2	4	no	—
171	C₂²×C₄×C₄₁	—	4	2	no	—
172	C₂²×C₄×C₄₁	—	4	2	no	—
173	C₂²×C₄×C₄₁	—	4	2	no	—
174	C₂²×C₄×C₄₁	—	4	2	no	—
175	C₂²×C₄×C₄₁	—	4	2	no	—
176	C₂²×C₄×C₄₁	—	4	2	no	—
177	C₂²×C₄×C₄₁	—	4	2	no	—
178	C₂²×C₄×C₄₁	—	4	2	no	—
179	C₂²×C₄×C₄₁	—	4	2	no	—
180	C₂²×C₄×C₄₁	—	4	2	no	—
181	C₂²×C₄×C₄₁	—	4	2	no	—
182	C₂²×C₄×C₄₁	—	4	4	no	—
183	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
211	M₁₆×C₄₁	—	4	4	no	—
212	M₁₆×C₄₁	—	4	4	no	—
213	C₂×C₈×C₄₁	—	2	4	no	—
214	C₂×C₈×C₄₁	—	4	4	no	—
215	C₄⋊C₄×C₄₁	—	2	2	no	—
216	C₄⋊C₄×C₄₁	—	2	2	no	—
217	C₄⋊C₄×C₄₁	—	2	2	no	—
218	C₄⋊C₄×C₄₁	—	2	1	no	—
219	C₄⋊C₄×C₄₁	—	2	1	no	—
220	C₄⋊C₄×C₄₁	—	2	2	no	—
221	C₄⋊C₄×C₄₁	—	4	4	no	—
222	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
223	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
224	C₂²⋊C₄×C₄₁	—	2	2	no	—
225	C₂²⋊C₄×C₄₁	—	2	2	no	—
226	C₂²⋊C₄×C₄₁	—	2	2	no	—
227	C₂²⋊C₄×C₄₁	—	2	2	no	—
228	C₂²⋊C₄×C₄₁	—	2	2	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	2	no	—
234	C₂²⋊C₄×C₄₁	—	4	4	no	—
235	C₂²⋊C₄×C₄₁	—	4	4	no	—
236	C₂²⋊C₄×C₄₁	—	4	4	no	—
237	C₄²×C₄₁	—	2	2	no	—
238	C₄²×C₄₁	—	2	2	no	—
239	C₄²×C₄₁	—	4	4	no	—
240	C₂³×C₄₁	—	2	2	no	—
241	C₂³×C₄₁	—	2	2	no	—
242	C₂³×C₄₁	—	2	2	no	—
243	C₂³×C₄₁	—	2	2	no	—
244	C₂³×C₄₁	—	2	2	no	—
245	C₂³×C₄₁	—	2	2	no	—
246	C₂³×C₄₁	—	2	2	no	—
247	C₂³×C₄₁	—	2	2	no	—
248	C₂³×C₄₁	—	2	2	no	—
249	C₂³×C₄₁	—	2	2	no	—
250	C₂³×C₄₁	—	4	1	no	—
251	C₂³×C₄₁	—	4	1	no	—
252	C₂³×C₄₁	—	4	1	no	—
253	C₂³×C₄₁	—	4	1	no	—
254	C₂³×C₄₁	—	4	1	no	—
255	C₂³×C₄₁	—	4	1	no	—
256	C₂³×C₄₁	—	4	1	no	—
257	C₂³×C₄₁	—	4	1	no	—
258	C₂³×C₄₁	—	4	1	no	—
259	C₂³×C₄₁	—	4	1	no	—
260	C₂³×C₄₁	—	4	1	no	—
261	C₂³×C₄₁	—	4	1	no	—
262	C₂³×C₄₁	—	4	2	no	—
263	C₂³×C₄₁	—	4	2	no	—
264	C₂³×C₄₁	—	4	16	no	—
265	C₂³×C₄₁	—	4	2	no	—
266	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₄₁	—	4	2	no	—
274	Q₈×C₄₁	—	4	2	no	—
275	D₄×C₄₁	—	4	2	no	—
276	D₄×C₄₁	—	4	2	no	—
277	D₄×C₄₁	—	4	4	no	—
278	D₄×C₄₁	—	4	4	no	—
279	D₄×C₄₁	—	4	4	no	—
280	D₄×C₄₁	—	4	4	no	—
281	D₄×C₄₁	—	4	4	no	—
282	D₄×C₄₁	—	4	4	no	—
283	C₂×C₄×C₄₁	—	2	2	no	—
284	C₂×C₄×C₄₁	—	2	2	no	—
285	C₂×C₄×C₄₁	—	2	2	no	—
286	C₂×C₄×C₄₁	—	2	2	no	—
287	C₂×C₄×C₄₁	—	2	2	no	—
288	C₂×C₄×C₄₁	—	2	2	no	—
289	C₂×C₄×C₄₁	—	2	2	no	—
290	C₂×C₄×C₄₁	—	2	2	no	—
291	C₂×C₄×C₄₁	—	2	2	no	—
292	C₂×C₄×C₄₁	—	2	2	no	—
293	C₂×C₄×C₄₁	—	2	2	no	—
294	C₂×C₄×C₄₁	—	2	2	no	—
295	C₂×C₄×C₄₁	—	2	2	no	—
296	C₂×C₄×C₄₁	—	2	2	no	—
297	C₂×C₄×C₄₁	—	2	2	no	—
298	C₂×C₄×C₄₁	—	2	2	no	—
299	C₂×C₄×C₄₁	—	2	2	no	—
300	C₂×C₄×C₄₁	—	2	2	no	—
301	C₂×C₄×C₄₁	—	4	1	no	—
302	C₂×C₄×C₄₁	—	4	1	no	—
303	C₂×C₄×C₄₁	—	4	1	no	—
304	C₂×C₄×C₄₁	—	4	1	no	—
305	C₂×C₄×C₄₁	—	4	1	no	—
306	C₂×C₄×C₄₁	—	4	1	no	—
307	C₂×C₄×C₄₁	—	4	1	no	—
308	C₂×C₄×C₄₁	—	4	1	no	—
309	C₂×C₄×C₄₁	—	4	1	no	—
310	C₂×C₄×C₄₁	—	4	1	no	—
311	C₂×C₄×C₄₁	—	4	1	no	—
312	C₂×C₄×C₄₁	—	4	1	no	—
313	C₂×C₄×C₄₁	—	4	2	no	—
314	C₂×C₄×C₄₁	—	4	2	no	—
315	C₂×C₄×C₄₁	—	4	2	no	—
316	C₂×C₄×C₄₁	—	4	4	no	—
317	C₂×C₄×C₄₁	—	4	4	no	—
318	C₂×C₄×C₄₁	—	4	4	no	—
319	C₂×C₄×C₄₁	—	4	4	no	—
320	C₂×C₄×C₄₁	—	4	4	no	—
321	C₂×C₄×C₄₁	#99	1	4	yes	—
322	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
327	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
329	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
330	C₈×C₄₁	—	4	4	no	—
331	#17559	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂²×C₄₁	—	2	1	no	—
333	C₂²×C₄₁	—	2	1	no	—
334	C₂²×C₄₁	—	2	1	no	—
335	C₂²×C₄₁	—	2	1	no	—
336	C₂²×C₄₁	—	2	1	no	—
337	C₂²×C₄₁	—	2	1	no	—
338	C₂²×C₄₁	—	2	1	no	—
339	C₂²×C₄₁	—	2	1	no	—
340	C₂²×C₄₁	—	2	1	no	—
341	C₂²×C₄₁	—	2	1	no	—
342	C₂²×C₄₁	—	2	1	no	—
343	C₂²×C₄₁	—	2	1	no	—
344	C₂²×C₄₁	—	2	1	no	—
345	C₂²×C₄₁	—	2	1	no	—
346	C₂²×C₄₁	—	2	1	no	—
347	C₂²×C₄₁	—	2	1	no	—
348	C₂²×C₄₁	—	2	1	no	—
349	C₂²×C₄₁	—	2	1	no	—
350	C₂²×C₄₁	—	4	4	no	—
351	C₂²×C₄₁	—	4	4	no	—
352	C₂²×C₄₁	—	4	4	no	—
353	C₂²×C₄₁	—	4	4	no	—
354	C₂²×C₄₁	—	4	4	no	—
355	C₂²×C₄₁	—	4	4	no	—
356	C₂²×C₄₁	—	4	4	no	—
357	C₂²×C₄₁	—	4	2	no	—
358	C₂²×C₄₁	—	4	2	no	—
359	C₂²×C₄₁	—	4	2	no	—
360	C₂²×C₄₁	—	8	4	no	—
361	C₂²×C₄₁	C₂×#99	1	2	yes	—
362	C₂²×C₄₁	#421	1	2	yes	—
363	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
364	C₂²×C₄₁	#575	1	2	yes	—
365	C₄×C₄₁	—	2	1	no	—
366	C₄×C₄₁	—	2	1	no	—
367	C₄×C₄₁	—	2	1	no	—
368	C₄×C₄₁	—	2	1	no	—
369	C₄×C₄₁	—	2	1	no	—
370	C₄×C₄₁	—	2	1	no	—
371	C₄×C₄₁	—	4	2	no	—
372	C₄×C₄₁	—	4	2	no	—
373	C₄×C₄₁	—	4	2	no	—
374	C₄×C₄₁	—	8	4	no	—
375	C₄×C₄₁	C₂×#99	1	2	yes	—
376	C₄×C₄₁	C₂×#99	1	2	yes	—
377	C₂×#525	C₂×C₄₁	1	1	yes	characteristic
378	C₂×#407	C₂×C₄₁	1	1	yes	characteristic, complemented
379	#2280	C₂×C₄₁	1	1	yes	characteristic, complemented
380	#1513	C₂×C₄₁	1	4	yes	complemented
381	#1511	C₂×C₄₁	1	2	yes	complemented
382	#1510	C₂×C₄₁	1	2	yes	complemented
383	#1501	C₂×C₄₁	1	4	yes	complemented
384	C₂×C₄₁	—	2	2	no	—
385	C₂×C₄₁	—	2	2	no	—
386	C₂×C₄₁	—	2	2	no	—
387	C₂×C₄₁	—	4	1	no	—
388	C₂×C₄₁	—	4	1	no	—
389	C₂×C₄₁	—	4	1	no	—
390	C₂×C₄₁	—	4	1	no	—
391	C₂×C₄₁	—	8	2	no	—
392	C₂×C₄₁	C₂²×#99	1	1	yes	characteristic
393	C₂×C₄₁	#2896	1	1	yes	characteristic
394	C₂×C₄₁	C₂×#421	1	1	yes	characteristic
395	C₂²×#41	C₄×C₄₁	1	1	yes	characteristic, complemented
396	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
397	C₂²×M₁₆	—	2	1	no	—
398	#525	—	2	1	no	—
399	#525	—	2	1	no	—
400	#525	—	2	1	no	—
401	#525	—	2	1	no	—
402	#525	C₄×C₄₁	1	2	yes	complemented
403	#525	C₄×C₄₁	1	2	yes	complemented
404	#525	C₂²×C₄₁	1	2	yes	—
405	#525	C₂²×C₄₁	1	2	yes	—
406	C₂×#123	—	2	1	no	—
407	C₂×C₂²⋊Q₈	C₄×C₄₁	1	1	yes	characteristic, complemented
408	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
409	C₂×#121	C₄×C₄₁	1	1	yes	characteristic, complemented
410	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
411	C₂×#120	—	2	1	no	—
412	C₂×C₄×D₄	—	2	1	no	—
413	C₂×C₄×D₄	—	2	1	no	—
414	C₂×#117	—	2	1	no	—
415	C₂×#117	C₄×C₄₁	1	1	yes	characteristic, complemented
416	#407	—	2	1	no	—
417	#407	—	2	1	no	—
418	#407	C₂²×C₄₁	1	2	yes	—
419	#407	C₂²×C₄₁	1	2	yes	complemented
420	C₂×C₂²⋊C₈	—	2	1	no	—
421	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
422	#381	C₂²×C₄₁	1	2	yes	—
423	#380	—	2	1	no	—
424	#380	C₂²×C₄₁	1	2	yes	complemented
425	#379	—	2	1	no	—
426	C₄×C₂²⋊C₄	—	2	1	no	—
427	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	complemented
428	#328	C₂²×C₄₁	1	8	yes	complemented
429	#327	C₂²×C₄₁	1	8	yes	complemented
430	C₄₁	#17559	1	1	yes	characteristic, direct product factor, Sylow
431	C₂⁵	D₄×C₄₁	1	1	yes	characteristic
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	4	4	no	—
435	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
436	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
437	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
438	C₂²×D₄	—	2	1	no	—
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	—	2	1	no	—
441	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	4	4	no	—
444	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
445	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
446	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
447	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
448	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
449	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
450	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
451	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
452	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
453	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
454	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
458	C₂×M₁₆	—	2	2	no	—
459	C₂×M₁₆	—	2	2	no	—
460	C₂×M₁₆	—	4	4	no	—
461	C₂²×C₈	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	#123	—	2	2	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
471	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
472	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
473	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
474	#121	—	2	1	no	—
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	#121	C₂×C₄×C₄₁	1	2	yes	—
479	#121	C₂×C₄×C₄₁	1	2	yes	—
480	#121	C₂×C₄×C₄₁	1	2	yes	—
481	#121	C₂³×C₄₁	1	2	yes	—
482	#120	—	2	2	no	—
483	#120	—	2	2	no	—
484	#120	—	2	2	no	—
485	#120	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	#117	—	2	1	no	—
495	#117	—	2	1	no	—
496	#117	—	4	4	no	—
497	#117	C₂×C₄×C₄₁	1	2	yes	—
498	#117	C₂×C₄×C₄₁	1	2	yes	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	2	no	—
510	C₂×C₂²⋊C₄	—	2	2	no	—
511	C₂×C₂²⋊C₄	—	2	2	no	—
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	—	2	2	no	—
514	C₂²⋊C₈	—	2	2	no	—
515	C₂²⋊C₈	—	2	2	no	—
516	C₂²⋊C₈	—	2	2	no	—
517	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
518	#95	—	2	2	no	—
519	#95	C₂³×C₄₁	1	4	yes	—
520	C₂⁴	—	2	1	no	—
521	C₂⁴	—	4	2	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	—	4	2	no	—
524	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
525	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
526	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
527	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
528	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
529	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
530	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
531	#41	—	4	4	no	—
532	#41	—	4	4	no	—
533	#41	—	4	4	no	—
534	#41	—	4	4	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	4	2	no	—
537	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
572	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
573	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
574	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
575	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
576	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
577	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
578	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
579	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
580	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
581	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
582	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
583	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
584	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
585	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
586	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
587	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
588	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
599	M₁₆	—	4	4	no	—
600	M₁₆	—	4	4	no	—
601	C₂×C₈	—	2	4	no	—
602	C₂×C₈	—	4	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	4	4	no	—
610	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
611	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	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	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	4	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	16	no	—
653	C₂³	—	4	2	no	—
654	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
655	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
656	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
657	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
658	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
659	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
660	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
661	Q₈	—	4	2	no	—
662	Q₈	—	4	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	4	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	4	no	—
668	D₄	—	4	4	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	#99×C₄₁	1	4	yes	—
710	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
711	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
712	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
713	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
714	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
715	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
716	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
718	C₈	—	4	4	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	8	4	no	—
748	C₂²	C₂×#99×C₄₁	1	2	yes	—
749	C₂²	C₄₁×#421	1	2	yes	—
750	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
751	C₂²	C₄₁×#575	1	2	yes	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	8	4	no	—
762	C₄	C₂×#99×C₄₁	1	2	yes	—
763	C₄	C₂×#99×C₄₁	1	2	yes	—
764	C₂	—	2	2	no	—
765	C₂	—	2	2	no	—
766	C₂	—	2	2	no	—
767	C₂	—	4	1	no	—
768	C₂	—	4	1	no	—
769	C₂	—	4	1	no	—
770	C₂	—	4	1	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂²×#99×C₄₁	1	1	yes	characteristic
773	C₂	C₄₁×#2896	1	1	yes	characteristic
774	C₂	C₂×C₄₁×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₄₁×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂⁴×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#407	C₂	semidirect
3. C₄₁×#2280	C₂	semidirect
4. C₄₁×#1513	C₂	semidirect
5. C₄₁×#1511	C₂	semidirect
6. C₄₁×#1510	C₂	semidirect
7. C₄₁×#1501	C₂	semidirect
8. C₂²×#41×C₄₁	C₄	semidirect
15. C₄₁×#525	C₄	semidirect
16. C₄₁×#525	C₄	semidirect
20. C₂×C₂²⋊Q₈×C₄₁	C₄	semidirect
22. C₂×#121×C₄₁	C₄	semidirect
28. C₂×#117×C₄₁	C₄	semidirect
32. C₄₁×#407	C₂²	semidirect
34. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
37. C₄₁×#380	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
41. C₄₁×#328	C₂²	semidirect
42. C₄₁×#327	C₂²	semidirect
331. #17559	C₄₁	direct (N × H)
378. C₂×#407	C₂×C₄₁	semidirect
379. #2280	C₂×C₄₁	semidirect
380. #1513	C₂×C₄₁	semidirect
381. #1511	C₂×C₄₁	semidirect
382. #1510	C₂×C₄₁	semidirect
383. #1501	C₂×C₄₁	semidirect
395. C₂²×#41	C₄×C₄₁	semidirect
402. #525	C₄×C₄₁	semidirect
403. #525	C₄×C₄₁	semidirect
407. C₂×C₂²⋊Q₈	C₄×C₄₁	semidirect
409. C₂×#121	C₄×C₄₁	semidirect
415. C₂×#117	C₄×C₄₁	semidirect
419. #407	C₂²×C₄₁	semidirect
421. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
424. #380	C₂²×C₄₁	semidirect
427. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
428. #328	C₂²×C₄₁	semidirect
429. #327	C₂²×C₄₁	semidirect
430. C₄₁	#17559	direct (N × H)

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
C₂×C₄₁×#407	2
C₄₁×#2280	2
C₄₁×#1513	2
C₄₁×#1511	2
C₄₁×#1510	2
C₄₁×#1501	2
#17559	41

Subgroups — C41×#17559 #23793760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17559 #23793760