Subgroups — C₄₁×#14018 #23790219

Order 10496.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#385	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1439	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1439	C₂	1	2	yes	maximal, complemented
9	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₄₁	—	2	4	no	—
15	C₂×C₄×D₄×C₄₁	—	2	4	no	—
16	C₂×C₄×D₄×C₄₁	—	2	4	no	—
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#390	—	2	4	no	—
32	C₄₁×#390	C₄	1	8	yes	complemented
33	C₄₁×#389	—	2	4	no	—
34	C₄₁×#385	—	2	8	no	—
35	C₄×C₄⋊C₄×C₄₁	—	2	4	no	—
36	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#95×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×#95×C₄₁	C₂²	1	2	yes	—
39	C₂×#95×C₄₁	C₂²	1	2	yes	—
40	C₂×#95×C₄₁	C₂²	1	2	yes	—
41	C₂×#95×C₄₁	C₂²	1	2	yes	—
42	C₂×#95×C₄₁	C₂²	1	2	yes	—
43	C₂⁵×C₄₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	2	no	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	—	2	2	no	—
48	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
49	C₂²×D₄×C₄₁	D₄	1	4	yes	—
50	C₂²×D₄×C₄₁	Q₈	1	4	yes	—
51	C₂³×C₄×C₄₁	—	2	4	no	—
52	C₂³×C₄×C₄₁	—	2	4	no	—
53	C₂³×C₄×C₄₁	—	2	4	no	—
54	C₂³×C₄×C₄₁	—	2	4	no	—
55	C₂³×C₄×C₄₁	—	2	4	no	—
56	C₂³×C₄×C₄₁	—	4	2	no	—
57	C₂³×C₄×C₄₁	—	4	2	no	—
58	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
64	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₄₁	—	2	32	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
79	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
80	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
84	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	complemented
85	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	complemented
87	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
97	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
98	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
99	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
100	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	8	yes	complemented
101	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	8	yes	complemented
102	C₂×C₄²×C₄₁	—	2	2	no	—
103	C₂×C₄²×C₄₁	—	2	2	no	—
104	C₂×C₄²×C₄₁	—	2	2	no	—
105	C₂×C₄²×C₄₁	—	2	2	no	—
106	C₂×C₄²×C₄₁	—	2	2	no	—
107	C₂×C₄²×C₄₁	—	2	2	no	—
108	C₂×C₄²×C₄₁	—	2	2	no	—
109	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	complemented
110	C₂×C₄²×C₄₁	D₄	1	4	yes	—
111	#95×C₄₁	—	2	2	no	—
112	#95×C₄₁	—	2	2	no	—
113	#95×C₄₁	—	2	4	no	—
114	#95×C₄₁	—	2	4	no	—
115	#95×C₄₁	—	2	4	no	—
116	#95×C₄₁	—	4	2	no	—
117	#95×C₄₁	—	4	2	no	—
118	C₂⁴×C₄₁	—	2	2	no	—
119	C₂⁴×C₄₁	—	2	2	no	—
120	C₂⁴×C₄₁	—	2	2	no	—
121	C₂⁴×C₄₁	—	2	2	no	—
122	C₂⁴×C₄₁	—	2	2	no	—
123	C₂⁴×C₄₁	—	2	2	no	—
124	C₂⁴×C₄₁	—	2	2	no	—
125	C₂⁴×C₄₁	—	2	2	no	—
126	C₂⁴×C₄₁	—	2	2	no	—
127	C₂⁴×C₄₁	—	2	2	no	—
128	C₂⁴×C₄₁	—	2	2	no	—
129	C₂⁴×C₄₁	—	2	2	no	—
130	C₂⁴×C₄₁	C₂²×C₄	1	4	yes	—
131	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
132	C₂⁴×C₄₁	C₂×Q₈	1	4	yes	—
133	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₄₁	—	2	8	no	—
135	C₂×D₄×C₄₁	—	2	8	no	—
136	C₂×D₄×C₄₁	—	2	8	no	—
137	C₂×D₄×C₄₁	—	2	8	no	—
138	C₂×D₄×C₄₁	—	2	8	no	—
139	C₂×D₄×C₄₁	—	2	8	no	—
140	C₂×D₄×C₄₁	C₄⋊C₄	1	16	yes	complemented
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	1	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	1	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	1	no	—
149	C₂²×C₄×C₄₁	—	2	16	no	—
150	C₂²×C₄×C₄₁	—	2	1	no	—
151	C₂²×C₄×C₄₁	—	2	1	no	—
152	C₂²×C₄×C₄₁	—	2	1	no	—
153	C₂²×C₄×C₄₁	—	2	1	no	—
154	C₂²×C₄×C₄₁	—	2	2	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	1	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	2	1	no	—
160	C₂²×C₄×C₄₁	—	2	1	no	—
161	C₂²×C₄×C₄₁	—	2	1	no	—
162	C₂²×C₄×C₄₁	—	2	2	no	—
163	C₂²×C₄×C₄₁	—	2	2	no	—
164	C₂²×C₄×C₄₁	—	2	1	no	—
165	C₂²×C₄×C₄₁	—	2	2	no	—
166	C₂²×C₄×C₄₁	—	2	2	no	—
167	C₂²×C₄×C₄₁	—	2	1	no	—
168	C₂²×C₄×C₄₁	—	2	1	no	—
169	C₂²×C₄×C₄₁	—	2	1	no	—
170	C₂²×C₄×C₄₁	—	2	1	no	—
171	C₂²×C₄×C₄₁	—	2	2	no	—
172	C₂²×C₄×C₄₁	—	2	1	no	—
173	C₂²×C₄×C₄₁	—	2	1	no	—
174	C₂²×C₄×C₄₁	—	2	2	no	—
175	C₂²×C₄×C₄₁	—	2	2	no	—
176	C₂²×C₄×C₄₁	—	2	1	no	—
177	C₂²×C₄×C₄₁	—	2	1	no	—
178	C₂²×C₄×C₄₁	—	2	1	no	—
179	C₂²×C₄×C₄₁	—	2	1	no	—
180	C₂²×C₄×C₄₁	—	2	2	no	—
181	C₂²×C₄×C₄₁	—	2	1	no	—
182	C₂²×C₄×C₄₁	—	2	2	no	—
183	C₂²×C₄×C₄₁	—	2	1	no	—
184	C₂²×C₄×C₄₁	—	2	1	no	—
185	C₂²×C₄×C₄₁	—	2	1	no	—
186	C₂²×C₄×C₄₁	—	2	2	no	—
187	C₂²×C₄×C₄₁	—	2	2	no	—
188	C₂²×C₄×C₄₁	—	2	2	no	—
189	C₂²×C₄×C₄₁	—	2	2	no	—
190	C₂²×C₄×C₄₁	—	2	2	no	—
191	C₂²×C₄×C₄₁	—	2	2	no	—
192	C₂²×C₄×C₄₁	—	2	2	no	—
193	C₂²×C₄×C₄₁	—	4	8	no	—
194	C₂²×C₄×C₄₁	—	4	8	no	—
195	C₂²×C₄×C₄₁	—	4	8	no	—
196	C₂²×C₄×C₄₁	—	4	8	no	—
197	C₂²×C₄×C₄₁	—	4	8	no	—
198	C₂²×C₄×C₄₁	—	4	8	no	—
199	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
202	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
203	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
213	C₂²×C₄×C₄₁	#41	1	2	yes	—
214	C₂²×C₄×C₄₁	#41	1	2	yes	—
215	C₂²×C₄×C₄₁	#41	1	2	yes	—
216	C₂²×C₄×C₄₁	#41	1	2	yes	—
217	C₂²×C₄×C₄₁	#41	1	2	yes	—
218	C₄⋊C₄×C₄₁	—	2	8	no	—
219	C₄⋊C₄×C₄₁	—	2	8	no	—
220	C₄⋊C₄×C₄₁	—	2	8	no	—
221	C₄⋊C₄×C₄₁	—	2	8	no	—
222	C₄⋊C₄×C₄₁	—	4	8	no	—
223	C₄⋊C₄×C₄₁	—	4	4	no	—
224	C₂²⋊C₄×C₄₁	—	2	16	no	—
225	C₂²⋊C₄×C₄₁	—	2	16	no	—
226	C₂²⋊C₄×C₄₁	—	4	8	no	—
227	C₂²⋊C₄×C₄₁	—	4	8	no	—
228	C₂²⋊C₄×C₄₁	—	4	8	no	—
229	C₄²×C₄₁	—	2	8	no	—
230	C₄²×C₄₁	—	2	8	no	—
231	C₄²×C₄₁	—	4	4	no	—
232	C₂³×C₄₁	—	2	4	no	—
233	C₂³×C₄₁	—	2	4	no	—
234	C₂³×C₄₁	—	2	4	no	—
235	C₂³×C₄₁	—	2	4	no	—
236	C₂³×C₄₁	—	2	4	no	—
237	C₂³×C₄₁	—	2	4	no	—
238	C₂³×C₄₁	—	2	4	no	—
239	C₂³×C₄₁	—	2	4	no	—
240	C₂³×C₄₁	—	2	4	no	—
241	C₂³×C₄₁	—	2	4	no	—
242	C₂³×C₄₁	—	2	4	no	—
243	C₂³×C₄₁	—	2	4	no	—
244	C₂³×C₄₁	—	2	4	no	—
245	C₂³×C₄₁	—	2	4	no	—
246	C₂³×C₄₁	—	2	4	no	—
247	C₂³×C₄₁	—	2	4	no	—
248	C₂³×C₄₁	—	2	4	no	—
249	C₂³×C₄₁	—	2	4	no	—
250	C₂³×C₄₁	—	4	2	no	—
251	C₂³×C₄₁	—	4	2	no	—
252	C₂³×C₄₁	—	4	2	no	—
253	C₂³×C₄₁	—	4	2	no	—
254	C₂³×C₄₁	—	4	2	no	—
255	C₂³×C₄₁	—	4	2	no	—
256	C₂³×C₄₁	—	4	2	no	—
257	C₂³×C₄₁	—	4	2	no	—
258	C₂³×C₄₁	—	4	2	no	—
259	C₂³×C₄₁	—	4	2	no	—
260	C₂³×C₄₁	—	4	2	no	—
261	C₂³×C₄₁	—	4	2	no	—
262	C₂³×C₄₁	—	4	2	no	—
263	C₂³×C₄₁	—	4	2	no	—
264	C₂³×C₄₁	—	4	2	no	—
265	C₂³×C₄₁	—	4	2	no	—
266	C₂³×C₄₁	C₂×C₄⋊C₄	1	8	yes	—
267	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
268	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
269	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
270	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
271	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
272	C₂³×C₄₁	C₂²×Q₈	1	1	yes	characteristic
273	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
274	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
275	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
276	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
277	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
278	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
281	C₂³×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
282	D₄×C₄₁	—	2	32	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	4	no	—
297	C₂×C₄×C₄₁	—	2	4	no	—
298	C₂×C₄×C₄₁	—	2	2	no	—
299	C₂×C₄×C₄₁	—	2	4	no	—
300	C₂×C₄×C₄₁	—	2	2	no	—
301	C₂×C₄×C₄₁	—	2	2	no	—
302	C₂×C₄×C₄₁	—	2	4	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	4	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	—	4	32	no	—
314	C₂×C₄×C₄₁	—	4	1	no	—
315	C₂×C₄×C₄₁	—	4	1	no	—
316	C₂×C₄×C₄₁	—	4	2	no	—
317	C₂×C₄×C₄₁	—	4	1	no	—
318	C₂×C₄×C₄₁	—	4	1	no	—
319	C₂×C₄×C₄₁	—	4	2	no	—
320	C₂×C₄×C₄₁	—	4	1	no	—
321	C₂×C₄×C₄₁	—	4	1	no	—
322	C₂×C₄×C₄₁	—	4	1	no	—
323	C₂×C₄×C₄₁	—	4	1	no	—
324	C₂×C₄×C₄₁	—	4	2	no	—
325	C₂×C₄×C₄₁	—	4	2	no	—
326	C₂×C₄×C₄₁	—	4	1	no	—
327	C₂×C₄×C₄₁	—	4	1	no	—
328	C₂×C₄×C₄₁	—	4	1	no	—
329	C₂×C₄×C₄₁	—	4	2	no	—
330	C₂×C₄×C₄₁	—	4	1	no	—
331	C₂×C₄×C₄₁	—	4	1	no	—
332	C₂×C₄×C₄₁	—	4	1	no	—
333	C₂×C₄×C₄₁	—	4	2	no	—
334	C₂×C₄×C₄₁	—	4	2	no	—
335	C₂×C₄×C₄₁	—	4	1	no	—
336	C₂×C₄×C₄₁	—	4	1	no	—
337	C₂×C₄×C₄₁	—	4	2	no	—
338	C₂×C₄×C₄₁	—	4	2	no	—
339	C₂×C₄×C₄₁	—	4	2	no	—
340	C₂×C₄×C₄₁	—	4	2	no	—
341	C₂×C₄×C₄₁	—	4	2	no	—
342	C₂×C₄×C₄₁	—	4	2	no	—
343	C₂×C₄×C₄₁	—	4	2	no	—
344	C₂×C₄×C₄₁	—	4	2	no	—
345	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
346	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
347	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
348	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	complemented
349	C₂×C₄×C₄₁	#120	1	4	yes	—
350	C₂×C₄×C₄₁	#121	1	4	yes	—
351	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
352	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
353	C₂×C₄×C₄₁	#123	1	4	yes	—
354	#14018	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂²×C₄₁	—	2	8	no	—
356	C₂²×C₄₁	—	2	8	no	—
357	C₂²×C₄₁	—	2	8	no	—
358	C₂²×C₄₁	—	4	4	no	—
359	C₂²×C₄₁	—	4	4	no	—
360	C₂²×C₄₁	—	4	4	no	—
361	C₂²×C₄₁	—	4	4	no	—
362	C₂²×C₄₁	—	4	4	no	—
363	C₂²×C₄₁	—	4	4	no	—
364	C₂²×C₄₁	—	4	4	no	—
365	C₂²×C₄₁	—	4	4	no	—
366	C₂²×C₄₁	—	4	4	no	—
367	C₂²×C₄₁	—	4	4	no	—
368	C₂²×C₄₁	—	4	4	no	—
369	C₂²×C₄₁	—	4	4	no	—
370	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
371	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
372	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
373	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
375	C₂²×C₄₁	#518	1	1	yes	characteristic
376	C₂²×C₄₁	#520	1	1	yes	characteristic
377	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
378	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
379	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
380	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
381	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
382	C₂²×C₄₁	#525	1	1	yes	characteristic
383	C₂²×C₄₁	#529	1	1	yes	characteristic
384	C₂²×C₄₁	#532	1	1	yes	characteristic
385	C₂²×C₄₁	#535	1	1	yes	characteristic
386	C₂²×C₄₁	#537	1	1	yes	characteristic
387	C₂²×C₄₁	#540	1	1	yes	characteristic
388	C₂²×C₄₁	#542	1	1	yes	characteristic
389	C₂²×C₄₁	D₄²	1	1	yes	characteristic
390	C₂²×C₄₁	D₄²	1	1	yes	characteristic
391	C₂²×C₄₁	#546	1	1	yes	characteristic
392	C₂²×C₄₁	#546	1	1	yes	characteristic
393	C₂²×C₄₁	#546	1	1	yes	characteristic
394	C₂²×C₄₁	#547	1	1	yes	characteristic
395	C₂²×C₄₁	#548	1	1	yes	characteristic
396	C₂²×C₄₁	D₄×Q₈	1	1	yes	characteristic
397	C₂²×C₄₁	#550	1	1	yes	characteristic
398	C₂²×C₄₁	#550	1	1	yes	characteristic
399	C₂²×C₄₁	#554	1	1	yes	characteristic
400	C₂²×C₄₁	#554	1	1	yes	characteristic
401	C₂²×C₄₁	#554	1	1	yes	characteristic
402	C₂²×C₄₁	#556	1	1	yes	characteristic
403	C₂²×C₄₁	#559	1	1	yes	characteristic
404	C₂²×C₄₁	#559	1	1	yes	characteristic
405	C₄×C₄₁	—	2	4	no	—
406	C₄×C₄₁	—	2	4	no	—
407	C₄×C₄₁	—	4	2	no	—
408	C₄×C₄₁	—	4	4	no	—
409	C₄×C₄₁	—	4	2	no	—
410	C₄×C₄₁	—	4	2	no	—
411	C₄×C₄₁	—	4	2	no	—
412	C₄×C₄₁	—	4	4	no	—
413	C₄×C₄₁	—	8	2	no	—
414	C₄×C₄₁	#385	1	8	yes	complemented
415	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic
416	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
417	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
418	C₂×#389	C₂×C₄₁	1	1	yes	characteristic, complemented
419	C₂×#385	C₂×C₄₁	1	2	yes	complemented
420	C₂×C₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
421	#1439	C₂×C₄₁	1	2	yes	complemented
422	#1439	C₂×C₄₁	1	2	yes	complemented
423	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic, complemented
424	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic, complemented
425	C₂²⋊#95	C₂×C₄₁	1	2	yes	complemented
426	C₂×C₄₁	—	4	8	no	—
427	C₂×C₄₁	C₂×#385	1	1	yes	characteristic
428	C₂×C₄₁	C₄×#121	1	1	yes	characteristic
429	C₂×C₄₁	#2324	1	1	yes	characteristic
430	C₂×C₄₁	D₄×C₄⋊C₄	1	1	yes	characteristic
431	C₂×C₄₁	#2349	1	1	yes	characteristic
432	C₂×C₄₁	#2366	1	1	yes	characteristic
433	C₂×C₄₁	#2367	1	1	yes	characteristic
434	C₂×C₄₁	#2407	1	1	yes	characteristic
435	C₂×C₄₁	#2408	1	1	yes	characteristic
436	C₂×C₄₁	#2445	1	1	yes	characteristic
437	C₂×C₄₁	#2447	1	1	yes	characteristic
438	C₂×C₄₁	#2452	1	1	yes	characteristic
439	C₂×C₄₁	#2454	1	1	yes	characteristic
440	C₂×C₄₁	#2538	1	1	yes	characteristic
441	C₂×C₄₁	#2580	1	1	yes	characteristic
442	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
443	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
444	C₂×C₄×D₄	—	2	4	no	—
445	C₂×C₄×D₄	—	2	4	no	—
446	C₂×C₄×D₄	—	2	4	no	—
447	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
448	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
449	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
450	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
451	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
452	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
454	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
455	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
456	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
457	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
458	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
459	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
460	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
461	#390	—	2	4	no	—
462	#390	C₄×C₄₁	1	8	yes	complemented
463	#389	—	2	4	no	—
464	#385	—	2	8	no	—
465	C₄×C₄⋊C₄	—	2	4	no	—
466	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
467	C₂×#95	C₂²×C₄₁	1	2	yes	—
468	C₂×#95	C₂²×C₄₁	1	2	yes	—
469	C₂×#95	C₂²×C₄₁	1	2	yes	—
470	C₂×#95	C₂²×C₄₁	1	1	yes	characteristic
471	C₂×#95	C₂²×C₄₁	1	2	yes	—
472	C₂×#95	C₂²×C₄₁	1	2	yes	—
473	C₄₁	#14018	1	1	yes	characteristic, direct product factor, Sylow
474	C₂⁵	C₂³×C₄₁	1	2	yes	—
475	C₂²×D₄	—	2	2	no	—
476	C₂²×D₄	—	2	2	no	—
477	C₂²×D₄	—	2	2	no	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
480	C₂²×D₄	D₄×C₄₁	1	4	yes	—
481	C₂²×D₄	Q₈×C₄₁	1	4	yes	—
482	C₂³×C₄	—	2	4	no	—
483	C₂³×C₄	—	2	4	no	—
484	C₂³×C₄	—	2	4	no	—
485	C₂³×C₄	—	2	4	no	—
486	C₂³×C₄	—	2	4	no	—
487	C₂³×C₄	—	4	2	no	—
488	C₂³×C₄	—	4	2	no	—
489	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
490	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
491	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
495	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
499	C₄×D₄	—	2	32	no	—
500	C₂×C₄⋊C₄	—	2	2	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	2	2	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	4	no	—
510	C₂×C₄⋊C₄	—	2	4	no	—
511	C₂×C₄⋊C₄	—	2	2	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	—	4	2	no	—
515	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	complemented
516	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
517	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	complemented
518	C₂×C₂²⋊C₄	—	2	4	no	—
519	C₂×C₂²⋊C₄	—	2	4	no	—
520	C₂×C₂²⋊C₄	—	2	4	no	—
521	C₂×C₂²⋊C₄	—	2	4	no	—
522	C₂×C₂²⋊C₄	—	2	4	no	—
523	C₂×C₂²⋊C₄	—	2	4	no	—
524	C₂×C₂²⋊C₄	—	2	4	no	—
525	C₂×C₂²⋊C₄	—	2	4	no	—
526	C₂×C₂²⋊C₄	—	2	4	no	—
527	C₂×C₂²⋊C₄	—	4	2	no	—
528	C₂×C₂²⋊C₄	—	4	2	no	—
529	C₂×C₂²⋊C₄	—	4	2	no	—
530	C₂×C₂²⋊C₄	—	4	2	no	—
531	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	8	yes	complemented
532	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	8	yes	complemented
533	C₂×C₄²	—	2	2	no	—
534	C₂×C₄²	—	2	2	no	—
535	C₂×C₄²	—	2	2	no	—
536	C₂×C₄²	—	2	2	no	—
537	C₂×C₄²	—	2	2	no	—
538	C₂×C₄²	—	2	2	no	—
539	C₂×C₄²	—	2	2	no	—
540	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	complemented
541	C₂×C₄²	D₄×C₄₁	1	4	yes	—
542	#95	—	2	2	no	—
543	#95	—	2	2	no	—
544	#95	—	2	4	no	—
545	#95	—	2	4	no	—
546	#95	—	2	4	no	—
547	#95	—	4	2	no	—
548	#95	—	4	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	2	no	—
556	C₂⁴	—	2	2	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	2	2	no	—
561	C₂⁴	C₂²×C₄×C₄₁	1	4	yes	—
562	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
563	C₂⁴	C₂×Q₈×C₄₁	1	4	yes	—
564	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	2	8	no	—
570	C₂×D₄	—	2	8	no	—
571	C₂×D₄	C₄⋊C₄×C₄₁	1	16	yes	complemented
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	16	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	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	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	1	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	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	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	4	8	no	—
625	C₂²×C₄	—	4	8	no	—
626	C₂²×C₄	—	4	8	no	—
627	C₂²×C₄	—	4	8	no	—
628	C₂²×C₄	—	4	8	no	—
629	C₂²×C₄	—	4	8	no	—
630	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
631	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
632	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
633	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
635	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
636	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
637	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
638	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
639	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
640	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
641	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
642	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
643	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
644	C₂²×C₄	#41×C₄₁	1	2	yes	—
645	C₂²×C₄	#41×C₄₁	1	2	yes	—
646	C₂²×C₄	#41×C₄₁	1	2	yes	—
647	C₂²×C₄	#41×C₄₁	1	2	yes	—
648	C₂²×C₄	#41×C₄₁	1	2	yes	—
649	C₄⋊C₄	—	2	8	no	—
650	C₄⋊C₄	—	2	8	no	—
651	C₄⋊C₄	—	2	8	no	—
652	C₄⋊C₄	—	2	8	no	—
653	C₄⋊C₄	—	4	8	no	—
654	C₄⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	—	2	16	no	—
656	C₂²⋊C₄	—	2	16	no	—
657	C₂²⋊C₄	—	4	8	no	—
658	C₂²⋊C₄	—	4	8	no	—
659	C₂²⋊C₄	—	4	8	no	—
660	C₄²	—	2	8	no	—
661	C₄²	—	2	8	no	—
662	C₄²	—	4	4	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	C₂×C₄⋊C₄×C₄₁	1	8	yes	—
698	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
699	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
700	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
701	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
702	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
703	C₂³	C₂²×Q₈×C₄₁	1	1	yes	characteristic
704	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
705	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
706	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
707	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
708	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
709	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
710	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
711	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
712	C₂³	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
713	D₄	—	2	32	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	32	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
777	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
778	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
779	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	complemented
780	C₂×C₄	#120×C₄₁	1	4	yes	—
781	C₂×C₄	#121×C₄₁	1	4	yes	—
782	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
783	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
784	C₂×C₄	#123×C₄₁	1	4	yes	—
785	C₂²	—	2	8	no	—
786	C₂²	—	2	8	no	—
787	C₂²	—	2	8	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	4	4	no	—
800	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
801	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
802	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
803	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
804	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
805	C₂²	C₄₁×#518	1	1	yes	characteristic
806	C₂²	C₄₁×#520	1	1	yes	characteristic
807	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
808	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
809	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
810	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
811	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
812	C₂²	C₄₁×#525	1	1	yes	characteristic
813	C₂²	C₄₁×#529	1	1	yes	characteristic
814	C₂²	C₄₁×#532	1	1	yes	characteristic
815	C₂²	C₄₁×#535	1	1	yes	characteristic
816	C₂²	C₄₁×#537	1	1	yes	characteristic
817	C₂²	C₄₁×#540	1	1	yes	characteristic
818	C₂²	C₄₁×#542	1	1	yes	characteristic
819	C₂²	D₄²×C₄₁	1	1	yes	characteristic
820	C₂²	D₄²×C₄₁	1	1	yes	characteristic
821	C₂²	C₄₁×#546	1	1	yes	characteristic
822	C₂²	C₄₁×#546	1	1	yes	characteristic
823	C₂²	C₄₁×#546	1	1	yes	characteristic
824	C₂²	C₄₁×#547	1	1	yes	characteristic
825	C₂²	C₄₁×#548	1	1	yes	characteristic
826	C₂²	D₄×Q₈×C₄₁	1	1	yes	characteristic
827	C₂²	C₄₁×#550	1	1	yes	characteristic
828	C₂²	C₄₁×#550	1	1	yes	characteristic
829	C₂²	C₄₁×#554	1	1	yes	characteristic
830	C₂²	C₄₁×#554	1	1	yes	characteristic
831	C₂²	C₄₁×#554	1	1	yes	characteristic
832	C₂²	C₄₁×#556	1	1	yes	characteristic
833	C₂²	C₄₁×#559	1	1	yes	characteristic
834	C₂²	C₄₁×#559	1	1	yes	characteristic
835	C₄	—	2	4	no	—
836	C₄	—	2	4	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	4	no	—
842	C₄	—	4	2	no	—
843	C₄	—	8	2	no	—
844	C₄	C₄₁×#385	1	8	yes	complemented
845	C₂	—	4	8	no	—
846	C₂	C₂×C₄₁×#385	1	1	yes	characteristic
847	C₂	C₄×#121×C₄₁	1	1	yes	characteristic
848	C₂	C₄₁×#2324	1	1	yes	characteristic
849	C₂	D₄×C₄⋊C₄×C₄₁	1	1	yes	characteristic
850	C₂	C₄₁×#2349	1	1	yes	characteristic
851	C₂	C₄₁×#2366	1	1	yes	characteristic
852	C₂	C₄₁×#2367	1	1	yes	characteristic
853	C₂	C₄₁×#2407	1	1	yes	characteristic
854	C₂	C₄₁×#2408	1	1	yes	characteristic
855	C₂	C₄₁×#2445	1	1	yes	characteristic
856	C₂	C₄₁×#2447	1	1	yes	characteristic
857	C₂	C₄₁×#2452	1	1	yes	characteristic
858	C₂	C₄₁×#2454	1	1	yes	characteristic
859	C₂	C₄₁×#2538	1	1	yes	characteristic
860	C₂	C₄₁×#2580	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂⁴	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₁×#389	C₂	semidirect
5. C₂×C₄₁×#385	C₂	semidirect
6. C₂×C₄×C₄⋊C₄×C₄₁	C₂	semidirect
7. C₄₁×#1439	C₂	semidirect
8. C₄₁×#1439	C₂	semidirect
9. C₄₁×C₄⋊#95	C₂	semidirect
10. C₄₁×C₄⋊#95	C₂	semidirect
11. C₄₁×C₂²⋊#95	C₂	semidirect
32. C₄₁×#390	C₄	semidirect
84. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
86. C₂×C₄⋊C₄×C₄₁	D₄	semidirect
100. C₂×C₂²⋊C₄×C₄₁	C₂×C₄	semidirect
101. C₂×C₂²⋊C₄×C₄₁	C₂×C₄	semidirect
109. C₂×C₄²×C₄₁	C₂×C₄	semidirect
140. C₂×D₄×C₄₁	C₄⋊C₄	semidirect
348. C₂×C₄×C₄₁	C₄×D₄	semidirect
354. #14018	C₄₁	direct (N × H)
414. C₄×C₄₁	#385	semidirect
418. C₂×#389	C₂×C₄₁	semidirect
419. C₂×#385	C₂×C₄₁	semidirect
420. C₂×C₄×C₄⋊C₄	C₂×C₄₁	semidirect
421. #1439	C₂×C₄₁	semidirect
422. #1439	C₂×C₄₁	semidirect
423. C₄⋊#95	C₂×C₄₁	semidirect
424. C₄⋊#95	C₂×C₄₁	semidirect
425. C₂²⋊#95	C₂×C₄₁	semidirect
462. #390	C₄×C₄₁	semidirect
473. C₄₁	#14018	direct (N × H)
515. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
517. C₂×C₄⋊C₄	D₄×C₄₁	semidirect
531. C₂×C₂²⋊C₄	C₂×C₄×C₄₁	semidirect
532. C₂×C₂²⋊C₄	C₂×C₄×C₄₁	semidirect
540. C₂×C₄²	C₂×C₄×C₄₁	semidirect
571. C₂×D₄	C₄⋊C₄×C₄₁	semidirect
779. C₂×C₄	C₄×D₄×C₄₁	semidirect
844. C₄	C₄₁×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₁	2
C₂×C₄₁×#390	2
C₂×C₄₁×#389	2
C₂×C₄₁×#385	2
C₂×C₄×C₄⋊C₄×C₄₁	2
C₄₁×#1439	2
C₄₁×C₄⋊#95	2
C₄₁×C₂²⋊#95	2
#14018	41

Subgroups — C41×#14018 #23790219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#14018 #23790219