Subgroups — C₂×C₄₁×#3370 #23837513

Order 10496.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₂×C₄₁×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#559	C₂	semidirect
2. C₂×C₄₁×#554	C₂	semidirect
3. C₄₁×#3370	C₂	direct (N × H)
4. C₂×C₄₁×#490	C₂	semidirect
5. C₂×C₄₁×#489	C₂	semidirect
6. C₂×C₄₁×#488	C₂	semidirect
7. C₂×C₄₁×#479	C₂	semidirect
8. C₂×C₄₁×#478	C₂	semidirect
9. C₂×C₄₁×#474	C₂	semidirect
10. C₂×C₄₁×#463	C₂	semidirect
11. C₂×C₄₁×#463	C₂	semidirect
13. C₂×C₄₁×#446	C₂	semidirect
14. C₂×C₄₁×#442	C₂	semidirect
15. C₂×C₄₁×#440	C₂	semidirect
16. C₂×C₄×D₈×C₄₁	C₂	semidirect
21. C₄₁×#559	C₂²	semidirect
23. C₄₁×#554	C₂²	semidirect
45. C₄₁×#490	C₂²	semidirect
46. C₄₁×#489	C₂²	semidirect
47. C₄₁×#488	C₂²	semidirect
48. C₄₁×#479	C₂²	semidirect
49. C₄₁×#478	C₂²	semidirect
50. C₄₁×#474	C₂²	semidirect
51. C₄₁×#463	C₂²	semidirect
52. C₄₁×#463	C₂²	semidirect
54. C₄₁×#446	C₂²	semidirect
55. C₄₁×#442	C₂²	semidirect
56. C₄₁×#440	C₂²	semidirect
57. C₄×D₈×C₄₁	C₂²	semidirect
336. C₂×#3370	C₄₁	direct (N × H)
367. C₂×#559	C₂×C₄₁	semidirect
368. C₂×#554	C₂×C₄₁	semidirect
369. #3370	C₂×C₄₁	direct (N × H)
370. C₂×#490	C₂×C₄₁	semidirect
371. C₂×#489	C₂×C₄₁	semidirect
372. C₂×#488	C₂×C₄₁	semidirect
373. C₂×#479	C₂×C₄₁	semidirect
374. C₂×#478	C₂×C₄₁	semidirect
375. C₂×#474	C₂×C₄₁	semidirect
376. C₂×#463	C₂×C₄₁	semidirect
377. C₂×#463	C₂×C₄₁	semidirect
379. C₂×#446	C₂×C₄₁	semidirect
380. C₂×#442	C₂×C₄₁	semidirect
381. C₂×#440	C₂×C₄₁	semidirect
382. C₂×C₄×D₈	C₂×C₄₁	semidirect
386. C₂×C₄₁	#3370	direct (N × H)
394. #559	C₂²×C₄₁	semidirect
396. #554	C₂²×C₄₁	semidirect
418. #490	C₂²×C₄₁	semidirect
419. #489	C₂²×C₄₁	semidirect
420. #488	C₂²×C₄₁	semidirect
421. #479	C₂²×C₄₁	semidirect
422. #478	C₂²×C₄₁	semidirect
423. #474	C₂²×C₄₁	semidirect
424. #463	C₂²×C₄₁	semidirect
425. #463	C₂²×C₄₁	semidirect
427. #446	C₂²×C₄₁	semidirect
428. #442	C₂²×C₄₁	semidirect
429. #440	C₂²×C₄₁	semidirect
430. C₄×D₈	C₂²×C₄₁	semidirect
450. C₄₁	C₂×#3370	direct (N × H)
743. C₂	C₄₁×#3370	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×#559	2
C₂×C₄₁×#554	2
C₄₁×#3370	2
C₂×C₄₁×#490	2
C₂×C₄₁×#489	2
C₂×C₄₁×#488	2
C₂×C₄₁×#479	2
C₂×C₄₁×#478	2
C₂×C₄₁×#474	2
C₂×C₄₁×#463	2
C₂×C₄₁×#459	2
C₂×C₄₁×#446	2
C₂×C₄₁×#442	2
C₂×C₄₁×#440	2
C₂×C₄×D₈×C₄₁	2
C₂×#3370	41

Subgroups — C2×C41×#3370 #23837513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3370 #23837513