Subgroups — C₂×C₄₁×#3121 #23836751

Order 10496.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3121	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#482	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#448	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#542	—	2	4	no	—
23	C₄₁×#542	C₂²	1	8	yes	—
24	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#126×C₄₁	—	2	1	no	—
26	C₂×#124×C₄₁	—	2	1	no	—
27	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#123×C₄₁	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
30	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#519	—	2	4	no	—
33	C₄₁×#519	C₂²	1	8	yes	complemented
34	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
35	C₂×C₄×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×Q₈×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#117×C₄₁	—	2	1	no	—
43	C₂×#117×C₄₁	—	2	1	no	—
44	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
46	C₄₁×#485	C₂²	1	8	yes	complemented
47	C₄₁×#482	C₂²	1	8	yes	—
48	C₄₁×#477	C₂²	1	8	yes	complemented
49	C₄₁×#475	C₂²	1	8	yes	complemented
50	C₄₁×#464	C₂²	1	8	yes	complemented
51	C₄₁×#464	C₂²	1	8	yes	complemented
52	C₄₁×#451	C₂²	1	8	yes	complemented
53	C₄₁×#448	C₂²	1	8	yes	—
54	C₄₁×#441	C₂²	1	8	yes	complemented
55	C₄₁×#440	C₂²	1	8	yes	complemented
56	C₄×Q₁₆×C₄₁	C₂²	1	8	yes	complemented
57	C₄×SD₁₆×C₄₁	C₂²	1	8	yes	complemented
58	C₄₁×#433	C₂²	1	8	yes	complemented
59	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
60	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
61	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
62	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×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×#103×C₄₁	C₂²	1	1	yes	characteristic
68	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
69	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
70	C₂×#103×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×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×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	4	no	—
78	C₂²×Q₈×C₄₁	—	2	4	no	—
79	C₂²×Q₈×C₄₁	—	2	1	no	—
80	C₂²×Q₈×C₄₁	—	2	2	no	—
81	C₂²×Q₈×C₄₁	—	2	1	no	—
82	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
84	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₁	—	2	1	no	—
87	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₁	—	2	1	no	—
89	C₂³×C₄×C₄₁	—	2	1	no	—
90	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
91	C₂×Q₁₆×C₄₁	—	2	4	no	—
92	C₂×Q₁₆×C₄₁	—	2	4	no	—
93	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
94	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₄₁	—	2	4	no	—
96	C₂×SD₁₆×C₄₁	—	2	4	no	—
97	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
99	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₄₁	—	2	2	no	—
104	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
105	#126×C₄₁	—	2	8	no	—
106	#124×C₄₁	—	2	8	no	—
107	#124×C₄₁	—	2	2	no	—
108	#124×C₄₁	C₂³	1	4	yes	—
109	#123×C₄₁	—	2	8	no	—
110	C₂²⋊Q₈×C₄₁	—	2	2	no	—
111	C₂²⋊Q₈×C₄₁	—	2	8	no	—
112	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
113	#121×C₄₁	—	2	2	no	—
114	#121×C₄₁	C₂³	1	4	yes	—
115	C₄×Q₈×C₄₁	—	2	8	no	—
116	C₄×Q₈×C₄₁	—	2	8	no	—
117	C₄×Q₈×C₄₁	—	2	2	no	—
118	C₄×Q₈×C₄₁	—	2	2	no	—
119	C₄×Q₈×C₄₁	—	2	2	no	—
120	C₄×Q₈×C₄₁	—	2	2	no	—
121	C₄×Q₈×C₄₁	—	2	2	no	—
122	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
123	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
124	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
125	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
126	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
127	C₄×D₄×C₄₁	—	2	2	no	—
128	C₄×D₄×C₄₁	C₂³	1	4	yes	—
129	#117×C₄₁	—	2	2	no	—
130	#117×C₄₁	—	2	8	no	—
131	#117×C₄₁	—	2	8	no	—
132	#117×C₄₁	D₄	1	4	yes	—
133	#117×C₄₁	C₂³	1	4	yes	—
134	#117×C₄₁	C₂³	1	4	yes	—
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	1	no	—
140	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
141	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
142	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₄₁	D₄	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×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
156	C₂×C₄²×C₄₁	—	2	1	no	—
157	C₂×C₄²×C₄₁	—	2	1	no	—
158	C₂×C₄²×C₄₁	—	2	1	no	—
159	C₂×C₄²×C₄₁	—	2	1	no	—
160	C₂×C₄²×C₄₁	—	2	1	no	—
161	C₂×C₄²×C₄₁	—	2	1	no	—
162	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
164	#107×C₄₁	C₂³	1	4	yes	—
165	#107×C₄₁	C₂³	1	4	yes	—
166	#106×C₄₁	C₂³	1	4	yes	—
167	#106×C₄₁	C₂³	1	4	yes	—
168	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
169	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
170	#103×C₄₁	C₂³	1	4	yes	—
171	#103×C₄₁	C₂³	1	4	yes	—
172	#103×C₄₁	C₂³	1	4	yes	—
173	#103×C₄₁	C₂³	1	4	yes	—
174	#103×C₄₁	C₂³	1	4	yes	—
175	#103×C₄₁	C₂³	1	4	yes	—
176	#102×C₄₁	C₂³	1	4	yes	—
177	#102×C₄₁	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
180	#97×C₄₁	C₂³	1	4	yes	—
181	C₄×C₈×C₄₁	C₂³	1	4	yes	—
182	C₂⁴×C₄₁	—	2	1	no	—
183	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₄₁	—	2	16	no	—
185	C₂×Q₈×C₄₁	—	2	8	no	—
186	C₂×Q₈×C₄₁	—	2	8	no	—
187	C₂×Q₈×C₄₁	—	2	8	no	—
188	C₂×Q₈×C₄₁	—	2	4	no	—
189	C₂×Q₈×C₄₁	—	2	1	no	—
190	C₂×Q₈×C₄₁	—	2	1	no	—
191	C₂×Q₈×C₄₁	—	2	1	no	—
192	C₂×Q₈×C₄₁	—	2	4	no	—
193	C₂×Q₈×C₄₁	—	2	2	no	—
194	C₂×Q₈×C₄₁	—	2	2	no	—
195	C₂×Q₈×C₄₁	—	2	2	no	—
196	C₂×Q₈×C₄₁	—	2	2	no	—
197	C₂×Q₈×C₄₁	—	8	2	no	—
198	C₂×Q₈×C₄₁	#41	1	4	yes	—
199	C₂×Q₈×C₄₁	#41	1	4	yes	—
200	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
201	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
203	C₂×D₄×C₄₁	—	2	4	no	—
204	C₂×D₄×C₄₁	—	2	1	no	—
205	C₂×D₄×C₄₁	—	2	2	no	—
206	C₂×D₄×C₄₁	—	2	2	no	—
207	C₂×D₄×C₄₁	—	8	2	no	—
208	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₄₁	—	2	8	no	—
210	C₂²×C₄×C₄₁	—	2	4	no	—
211	C₂²×C₄×C₄₁	—	2	1	no	—
212	C₂²×C₄×C₄₁	—	2	1	no	—
213	C₂²×C₄×C₄₁	—	2	2	no	—
214	C₂²×C₄×C₄₁	—	2	2	no	—
215	C₂²×C₄×C₄₁	—	2	1	no	—
216	C₂²×C₄×C₄₁	—	2	1	no	—
217	C₂²×C₄×C₄₁	—	2	1	no	—
218	C₂²×C₄×C₄₁	—	2	1	no	—
219	C₂²×C₄×C₄₁	—	2	1	no	—
220	C₂²×C₄×C₄₁	—	2	4	no	—
221	C₂²×C₄×C₄₁	—	8	2	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	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	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₄₁	—	2	8	no	—
231	Q₁₆×C₄₁	—	2	8	no	—
232	SD₁₆×C₄₁	—	2	8	no	—
233	SD₁₆×C₄₁	—	2	8	no	—
234	C₂×C₈×C₄₁	—	2	2	no	—
235	C₂×C₈×C₄₁	—	2	2	no	—
236	C₂×C₈×C₄₁	—	2	2	no	—
237	C₂×C₈×C₄₁	—	2	2	no	—
238	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
239	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
240	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
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	4	no	—
246	C₄⋊C₄×C₄₁	—	2	4	no	—
247	C₄⋊C₄×C₄₁	—	2	4	no	—
248	C₄⋊C₄×C₄₁	—	2	4	no	—
249	C₄⋊C₄×C₄₁	—	2	1	no	—
250	C₄⋊C₄×C₄₁	—	2	1	no	—
251	C₄⋊C₄×C₄₁	—	2	1	no	—
252	C₄⋊C₄×C₄₁	—	2	1	no	—
253	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
255	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
266	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
267	C₄²×C₄₁	—	2	4	no	—
268	C₄²×C₄₁	—	2	4	no	—
269	C₄²×C₄₁	—	2	4	no	—
270	C₄²×C₄₁	—	2	4	no	—
271	C₄²×C₄₁	—	2	4	no	—
272	C₄²×C₄₁	—	2	4	no	—
273	C₄²×C₄₁	C₂×D₄	1	2	yes	—
274	C₄²×C₄₁	C₂×D₄	1	2	yes	—
275	C₄²×C₄₁	C₂⁴	1	2	yes	—
276	C₄²×C₄₁	C₂⁴	1	2	yes	—
277	C₂³×C₄₁	—	2	2	no	—
278	C₂³×C₄₁	—	2	2	no	—
279	C₂³×C₄₁	—	2	2	no	—
280	C₂³×C₄₁	—	2	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	2	yes	—
285	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
286	Q₈×C₄₁	—	2	16	no	—
287	Q₈×C₄₁	—	2	4	no	—
288	Q₈×C₄₁	—	2	4	no	—
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	2	no	—
294	Q₈×C₄₁	—	8	4	no	—
295	Q₈×C₄₁	C₂×#41	1	4	yes	—
296	Q₈×C₄₁	C₂×#41	1	4	yes	—
297	D₄×C₄₁	—	2	2	no	—
298	D₄×C₄₁	—	2	2	no	—
299	D₄×C₄₁	—	4	2	no	—
300	D₄×C₄₁	—	8	4	no	—
301	C₂×C₄×C₄₁	—	2	16	no	—
302	C₂×C₄×C₄₁	—	2	4	no	—
303	C₂×C₄×C₄₁	—	2	4	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	4	no	—
312	C₂×C₄×C₄₁	—	2	2	no	—
313	C₂×C₄×C₄₁	—	2	2	no	—
314	C₂×C₄×C₄₁	—	2	2	no	—
315	C₂×C₄×C₄₁	—	2	2	no	—
316	C₂×C₄×C₄₁	—	2	2	no	—
317	C₂×C₄×C₄₁	—	2	2	no	—
318	C₂×C₄×C₄₁	—	2	2	no	—
319	C₂×C₄×C₄₁	—	4	2	no	—
320	C₂×C₄×C₄₁	—	4	2	no	—
321	C₂×C₄×C₄₁	—	4	2	no	—
322	C₂×C₄×C₄₁	—	4	2	no	—
323	C₂×C₄×C₄₁	—	4	2	no	—
324	C₂×C₄×C₄₁	—	8	4	no	—
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	2	yes	—
329	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
332	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
333	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
334	C₈×C₄₁	—	2	2	no	—
335	C₈×C₄₁	—	2	2	no	—
336	C₈×C₄₁	—	2	2	no	—
337	C₈×C₄₁	—	2	2	no	—
338	C₂×#3121	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₂²×C₄₁	—	2	2	no	—
340	C₂²×C₄₁	—	2	2	no	—
341	C₂²×C₄₁	—	2	2	no	—
342	C₂²×C₄₁	—	4	4	no	—
343	C₂²×C₄₁	—	4	2	no	—
344	C₂²×C₄₁	—	4	2	no	—
345	C₂²×C₄₁	—	4	2	no	—
346	C₂²×C₄₁	—	8	4	no	—
347	C₂²×C₄₁	#525	1	2	yes	—
348	C₂²×C₄₁	#577	1	2	yes	—
349	C₂²×C₄₁	#578	1	2	yes	—
350	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
351	C₄×C₄₁	—	2	4	no	—
352	C₄×C₄₁	—	2	4	no	—
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	—	4	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	#525	1	2	yes	—
364	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
365	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
366	C₂×#542	C₂×C₄₁	1	1	yes	characteristic
367	C₂×#519	C₂×C₄₁	1	1	yes	characteristic, complemented
368	#3121	C₂×C₄₁	1	16	yes	direct product factor
369	C₂×#485	C₂×C₄₁	1	1	yes	characteristic, complemented
370	C₂×#482	C₂×C₄₁	1	1	yes	characteristic
371	C₂×#477	C₂×C₄₁	1	1	yes	characteristic, complemented
372	C₂×#475	C₂×C₄₁	1	1	yes	characteristic, complemented
373	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
374	C₂×#464	C₂×C₄₁	1	1	yes	characteristic, complemented
375	C₂×#451	C₂×C₄₁	1	1	yes	characteristic, complemented
376	C₂×#448	C₂×C₄₁	1	1	yes	characteristic
377	C₂×#441	C₂×C₄₁	1	1	yes	characteristic, complemented
378	C₂×#440	C₂×C₄₁	1	1	yes	characteristic, complemented
379	C₂×C₄×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
380	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
381	C₂×#433	C₂×C₄₁	1	1	yes	characteristic, complemented
382	C₂×C₄₁	—	4	2	no	—
383	C₂×C₄₁	—	8	2	no	—
384	C₂×C₄₁	#3121	1	4	yes	direct product factor
385	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
386	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
387	C₂×C₄₁	C₂×#578	1	1	yes	characteristic
388	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
389	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
390	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
391	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
393	#542	—	2	4	no	—
394	#542	C₂²×C₄₁	1	8	yes	—
395	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
396	C₂×#126	—	2	1	no	—
397	C₂×#124	—	2	1	no	—
398	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
399	C₂×#123	—	2	1	no	—
400	C₂×C₂²⋊Q₈	—	2	1	no	—
401	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
402	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
403	#519	—	2	4	no	—
404	#519	C₂²×C₄₁	1	8	yes	complemented
405	C₂×C₄×Q₈	—	2	1	no	—
406	C₂×C₄×Q₈	—	2	1	no	—
407	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
413	C₂×#117	—	2	1	no	—
414	C₂×#117	—	2	1	no	—
415	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
416	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
417	#485	C₂²×C₄₁	1	8	yes	complemented
418	#482	C₂²×C₄₁	1	8	yes	—
419	#477	C₂²×C₄₁	1	8	yes	complemented
420	#475	C₂²×C₄₁	1	8	yes	complemented
421	#464	C₂²×C₄₁	1	8	yes	complemented
422	#464	C₂²×C₄₁	1	8	yes	complemented
423	#451	C₂²×C₄₁	1	8	yes	complemented
424	#448	C₂²×C₄₁	1	8	yes	—
425	#441	C₂²×C₄₁	1	8	yes	complemented
426	#440	C₂²×C₄₁	1	8	yes	complemented
427	C₄×Q₁₆	C₂²×C₄₁	1	8	yes	complemented
428	C₄×SD₁₆	C₂²×C₄₁	1	8	yes	complemented
429	#433	C₂²×C₄₁	1	8	yes	complemented
430	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
431	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
432	C₂×#106	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×#103	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×#103	C₂²×C₄₁	1	1	yes	characteristic
441	C₂×#103	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×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
446	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
447	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
448	C₄₁	C₂×#3121	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²×Q₈	—	2	4	no	—
450	C₂²×Q₈	—	2	4	no	—
451	C₂²×Q₈	—	2	1	no	—
452	C₂²×Q₈	—	2	2	no	—
453	C₂²×Q₈	—	2	1	no	—
454	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
456	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
463	C₂×Q₁₆	—	2	4	no	—
464	C₂×Q₁₆	—	2	4	no	—
465	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
466	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
467	C₂×SD₁₆	—	2	4	no	—
468	C₂×SD₁₆	—	2	4	no	—
469	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
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	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
477	#126	—	2	8	no	—
478	#124	—	2	8	no	—
479	#124	—	2	2	no	—
480	#124	C₂³×C₄₁	1	4	yes	—
481	#123	—	2	8	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
485	#121	—	2	2	no	—
486	#121	C₂³×C₄₁	1	4	yes	—
487	C₄×Q₈	—	2	8	no	—
488	C₄×Q₈	—	2	8	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
495	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
496	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
497	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
498	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	C₂³×C₄₁	1	4	yes	—
501	#117	—	2	2	no	—
502	#117	—	2	8	no	—
503	#117	—	2	8	no	—
504	#117	D₄×C₄₁	1	4	yes	—
505	#117	C₂³×C₄₁	1	4	yes	—
506	#117	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	1	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	C₂³×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×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₄₁	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	—	2	1	no	—
533	C₂×C₄²	—	2	1	no	—
534	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
536	#107	C₂³×C₄₁	1	4	yes	—
537	#107	C₂³×C₄₁	1	4	yes	—
538	#106	C₂³×C₄₁	1	4	yes	—
539	#106	C₂³×C₄₁	1	4	yes	—
540	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
541	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
542	#103	C₂³×C₄₁	1	4	yes	—
543	#103	C₂³×C₄₁	1	4	yes	—
544	#103	C₂³×C₄₁	1	4	yes	—
545	#103	C₂³×C₄₁	1	4	yes	—
546	#103	C₂³×C₄₁	1	4	yes	—
547	#103	C₂³×C₄₁	1	4	yes	—
548	#102	C₂³×C₄₁	1	4	yes	—
549	#102	C₂³×C₄₁	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
552	#97	C₂³×C₄₁	1	4	yes	—
553	C₄×C₈	C₂³×C₄₁	1	4	yes	—
554	C₂⁴	—	2	1	no	—
555	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
556	C₂×Q₈	—	2	16	no	—
557	C₂×Q₈	—	2	8	no	—
558	C₂×Q₈	—	2	8	no	—
559	C₂×Q₈	—	2	8	no	—
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	4	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	8	2	no	—
570	C₂×Q₈	#41×C₄₁	1	4	yes	—
571	C₂×Q₈	#41×C₄₁	1	4	yes	—
572	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
573	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
574	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	8	2	no	—
580	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	8	2	no	—
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	C₂×D₄×C₄₁	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
602	Q₁₆	—	2	8	no	—
603	Q₁₆	—	2	8	no	—
604	SD₁₆	—	2	8	no	—
605	SD₁₆	—	2	8	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
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	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
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	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
626	C₄⋊C₄	C₂×D₄×C₄₁	1	4	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	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
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	C₂×D₄×C₄₁	1	4	yes	—
638	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	C₂×D₄×C₄₁	1	2	yes	—
646	C₄²	C₂×D₄×C₄₁	1	2	yes	—
647	C₄²	C₂⁴×C₄₁	1	2	yes	—
648	C₄²	C₂⁴×C₄₁	1	2	yes	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
657	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
658	Q₈	—	2	16	no	—
659	Q₈	—	2	4	no	—
660	Q₈	—	2	4	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	2	2	no	—
665	Q₈	—	4	2	no	—
666	Q₈	—	8	4	no	—
667	Q₈	C₂×#41×C₄₁	1	4	yes	—
668	Q₈	C₂×#41×C₄₁	1	4	yes	—
669	D₄	—	2	2	no	—
670	D₄	—	2	2	no	—
671	D₄	—	4	2	no	—
672	D₄	—	8	4	no	—
673	C₂×C₄	—	2	16	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	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	4	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	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	8	4	no	—
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	C₂×#41×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	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	8	4	no	—
718	C₂²	C₄₁×#525	1	2	yes	—
719	C₂²	C₄₁×#577	1	2	yes	—
720	C₂²	C₄₁×#578	1	2	yes	—
721	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	4	no	—
728	C₄	—	2	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	C₄₁×#525	1	2	yes	—
735	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
736	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
737	C₂	—	4	2	no	—
738	C₂	—	8	2	no	—
739	C₂	C₄₁×#3121	1	4	yes	direct product factor
740	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
741	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
742	C₂	C₂×C₄₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#519	C₂	semidirect
3. C₄₁×#3121	C₂	direct (N × H)
4. C₂×C₄₁×#485	C₂	semidirect
6. C₂×C₄₁×#477	C₂	semidirect
7. C₂×C₄₁×#475	C₂	semidirect
8. C₂×C₄₁×#464	C₂	semidirect
9. C₂×C₄₁×#464	C₂	semidirect
10. C₂×C₄₁×#451	C₂	semidirect
12. C₂×C₄₁×#441	C₂	semidirect
13. C₂×C₄₁×#440	C₂	semidirect
14. C₂×C₄×Q₁₆×C₄₁	C₂	semidirect
15. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
16. C₂×C₄₁×#433	C₂	semidirect
33. C₄₁×#519	C₂²	semidirect
46. C₄₁×#485	C₂²	semidirect
48. C₄₁×#477	C₂²	semidirect
49. C₄₁×#475	C₂²	semidirect
50. C₄₁×#464	C₂²	semidirect
51. C₄₁×#464	C₂²	semidirect
52. C₄₁×#451	C₂²	semidirect
54. C₄₁×#441	C₂²	semidirect
55. C₄₁×#440	C₂²	semidirect
56. C₄×Q₁₆×C₄₁	C₂²	semidirect
57. C₄×SD₁₆×C₄₁	C₂²	semidirect
58. C₄₁×#433	C₂²	semidirect
338. C₂×#3121	C₄₁	direct (N × H)
367. C₂×#519	C₂×C₄₁	semidirect
368. #3121	C₂×C₄₁	direct (N × H)
369. C₂×#485	C₂×C₄₁	semidirect
371. C₂×#477	C₂×C₄₁	semidirect
372. C₂×#475	C₂×C₄₁	semidirect
373. C₂×#464	C₂×C₄₁	semidirect
374. C₂×#464	C₂×C₄₁	semidirect
375. C₂×#451	C₂×C₄₁	semidirect
377. C₂×#441	C₂×C₄₁	semidirect
378. C₂×#440	C₂×C₄₁	semidirect
379. C₂×C₄×Q₁₆	C₂×C₄₁	semidirect
380. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
381. C₂×#433	C₂×C₄₁	semidirect
384. C₂×C₄₁	#3121	direct (N × H)
404. #519	C₂²×C₄₁	semidirect
417. #485	C₂²×C₄₁	semidirect
419. #477	C₂²×C₄₁	semidirect
420. #475	C₂²×C₄₁	semidirect
421. #464	C₂²×C₄₁	semidirect
422. #464	C₂²×C₄₁	semidirect
423. #451	C₂²×C₄₁	semidirect
425. #441	C₂²×C₄₁	semidirect
426. #440	C₂²×C₄₁	semidirect
427. C₄×Q₁₆	C₂²×C₄₁	semidirect
428. C₄×SD₁₆	C₂²×C₄₁	semidirect
429. #433	C₂²×C₄₁	semidirect
448. C₄₁	C₂×#3121	direct (N × H)
739. C₂	C₄₁×#3121	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×#542	2
C₂×C₄₁×#519	2
C₄₁×#3121	2
C₂×C₄₁×#485	2
C₂×C₄₁×#482	2
C₂×C₄₁×#477	2
C₂×C₄₁×#475	2
C₂×C₄₁×#464	2
C₂×C₄₁×#451	2
C₂×C₄₁×#448	2
C₂×C₄₁×#441	2
C₂×C₄₁×#440	2
C₂×C₄×Q₁₆×C₄₁	2
C₂×C₄×SD₁₆×C₄₁	2
C₂×C₄₁×#433	2
C₂×#3121	41

Subgroups — C2×C41×#3121 #23836751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3121 #23836751