Subgroups — C₄₁×#21000 #23797201

Order 10496.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#575	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1906	C₂	1	8	yes	maximal, complemented
7	C₂×C₄₁×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#575	—	2	2	no	—
12	C₄₁×#575	—	2	2	no	—
13	C₄₁×#575	C₄	1	4	yes	complemented
14	C₄₁×#575	C₂²	1	4	yes	—
15	C₂×#137×C₄₁	—	2	1	no	—
16	C₂×#137×C₄₁	C₄	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
18	C₂×AGL(1,ℤ/8)×C₄₁	C₄	1	2	yes	complemented
19	C₂×#135×C₄₁	—	2	2	no	—
20	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#520	—	2	2	no	—
23	C₄₁×#520	—	2	2	no	—
24	C₄₁×#519	—	2	1	no	—
25	C₄₁×#518	—	2	1	no	—
26	C₄₁×#518	—	2	2	no	—
27	C₄×#41×C₄₁	—	2	2	no	—
28	C₄×#41×C₄₁	C₂²	1	4	yes	complemented
29	C₂×#117×C₄₁	—	2	2	no	—
30	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#421	—	2	2	no	—
34	C₄₁×#421	—	2	2	no	—
35	C₄₁×#421	—	2	2	no	—
36	C₄₁×#421	C₂²	1	4	yes	complemented
37	C₂×#104×C₄₁	—	2	2	no	—
38	C₂×#104×C₄₁	C₂²	1	4	yes	complemented
39	C₄₁×#410	—	2	2	no	—
40	C₄₁×#410	C₂²	1	4	yes	complemented
41	C₂×#99×C₄₁	—	2	2	no	—
42	C₄₁×#344	C₂²	1	4	yes	complemented
43	C₄₁×#339	C₂²	1	4	yes	complemented
44	C₂×#41×C₄₁	—	2	1	no	—
45	C₂×#41×C₄₁	—	2	1	no	—
46	C₂×#41×C₄₁	—	2	1	no	—
47	C₂×#41×C₄₁	—	2	1	no	—
48	C₂×#41×C₄₁	—	2	1	no	—
49	C₂×#41×C₄₁	—	2	1	no	—
50	C₂×#41×C₄₁	—	2	1	no	—
51	C₂×#41×C₄₁	—	2	1	no	—
52	C₂×#41×C₄₁	—	2	1	no	—
53	C₂×#41×C₄₁	—	2	1	no	—
54	C₂×#41×C₄₁	—	2	1	no	—
55	C₂×#41×C₄₁	—	2	1	no	—
56	C₂×#41×C₄₁	—	2	1	no	—
57	C₂×#41×C₄₁	—	2	1	no	—
58	C₂×#41×C₄₁	—	2	1	no	—
59	C₂×#41×C₄₁	—	2	1	no	—
60	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
61	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
62	C₂×#41×C₄₁	C₂×C₄	1	2	yes	complemented
63	C₂×#41×C₄₁	D₄	1	2	yes	—
64	C₂×#41×C₄₁	D₄	1	2	yes	—
65	C₂×#41×C₄₁	D₄	1	2	yes	—
66	C₂×#41×C₄₁	C₂³	1	2	yes	—
67	C₂×#41×C₄₁	C₂³	1	2	yes	—
68	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₄₁	—	2	1	no	—
71	C₂²×D₄×C₄₁	—	2	1	no	—
72	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₁	—	2	1	no	—
75	C₂³×C₄×C₄₁	—	2	1	no	—
76	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
77	#137×C₄₁	—	2	4	no	—
78	#137×C₄₁	—	2	4	no	—
79	#137×C₄₁	—	2	4	no	—
80	#137×C₄₁	C₂×C₄	1	8	yes	complemented
81	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
82	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
83	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
84	AGL(1,ℤ/8)×C₄₁	C₂×C₄	1	8	yes	complemented
85	#135×C₄₁	—	2	8	no	—
86	#135×C₄₁	—	2	8	no	—
87	C₂×Q₁₆×C₄₁	—	2	2	no	—
88	C₂×SD₁₆×C₄₁	—	2	2	no	—
89	C₂×SD₁₆×C₄₁	—	2	2	no	—
90	C₂×D₈×C₄₁	—	2	2	no	—
91	C₂×M₁₆×C₄₁	—	2	1	no	—
92	C₂×M₁₆×C₄₁	—	2	1	no	—
93	C₂×M₁₆×C₄₁	—	2	1	no	—
94	C₂×M₁₆×C₄₁	—	2	1	no	—
95	C₂×M₁₆×C₄₁	—	2	1	no	—
96	C₂×M₁₆×C₄₁	—	2	1	no	—
97	C₂×M₁₆×C₄₁	—	2	1	no	—
98	C₂×M₁₆×C₄₁	—	2	1	no	—
99	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	complemented
100	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	complemented
101	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
102	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
103	C₂²×C₈×C₄₁	—	2	1	no	—
104	C₂²×C₈×C₄₁	—	2	1	no	—
105	C₄×Q₈×C₄₁	—	2	4	no	—
106	C₄×Q₈×C₄₁	—	2	4	no	—
107	C₄×D₄×C₄₁	—	2	8	no	—
108	C₄×D₄×C₄₁	—	2	4	no	—
109	C₄×D₄×C₄₁	—	2	4	no	—
110	C₄×D₄×C₄₁	—	2	8	no	—
111	#117×C₄₁	—	2	4	no	—
112	#117×C₄₁	—	2	4	no	—
113	#117×C₄₁	—	2	1	no	—
114	#117×C₄₁	—	2	1	no	—
115	#117×C₄₁	—	2	1	no	—
116	#117×C₄₁	—	2	1	no	—
117	#117×C₄₁	—	2	1	no	—
118	#117×C₄₁	—	2	4	no	—
119	#117×C₄₁	—	2	1	no	—
120	#117×C₄₁	—	2	1	no	—
121	#117×C₄₁	D₄	1	2	yes	—
122	#117×C₄₁	D₄	1	2	yes	—
123	#117×C₄₁	D₄	1	2	yes	—
124	#117×C₄₁	C₂³	1	2	yes	—
125	#117×C₄₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
127	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
134	C₂×C₄²×C₄₁	—	2	1	no	—
135	C₂×C₄²×C₄₁	—	2	4	no	—
136	C₂×C₄²×C₄₁	—	2	1	no	—
137	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
138	#104×C₄₁	—	2	8	no	—
139	#104×C₄₁	—	2	8	no	—
140	#99×C₄₁	—	2	8	no	—
141	C₂⁴×C₄₁	—	2	1	no	—
142	C₂⁴×C₄₁	—	2	1	no	—
143	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
144	#41×C₄₁	—	2	2	no	—
145	#41×C₄₁	—	2	2	no	—
146	#41×C₄₁	—	2	2	no	—
147	#41×C₄₁	—	2	2	no	—
148	#41×C₄₁	—	2	2	no	—
149	#41×C₄₁	—	2	2	no	—
150	#41×C₄₁	—	2	2	no	—
151	#41×C₄₁	—	2	2	no	—
152	#41×C₄₁	—	2	2	no	—
153	#41×C₄₁	—	2	2	no	—
154	#41×C₄₁	—	2	2	no	—
155	#41×C₄₁	—	2	2	no	—
156	#41×C₄₁	—	2	2	no	—
157	#41×C₄₁	—	2	2	no	—
158	#41×C₄₁	—	2	2	no	—
159	#41×C₄₁	—	2	2	no	—
160	#41×C₄₁	—	2	2	no	—
161	#41×C₄₁	—	2	2	no	—
162	#41×C₄₁	—	2	2	no	—
163	#41×C₄₁	—	2	2	no	—
164	#41×C₄₁	—	4	1	no	—
165	#41×C₄₁	—	4	1	no	—
166	#41×C₄₁	—	4	1	no	—
167	#41×C₄₁	—	4	1	no	—
168	#41×C₄₁	—	4	1	no	—
169	#41×C₄₁	—	4	1	no	—
170	#41×C₄₁	—	4	1	no	—
171	#41×C₄₁	—	4	1	no	—
172	#41×C₄₁	C₂²⋊C₄	1	4	yes	—
173	#41×C₄₁	C₂²⋊C₄	1	4	yes	—
174	#41×C₄₁	C₂²×C₄	1	4	yes	—
175	#41×C₄₁	C₂×D₄	1	4	yes	—
176	C₂×Q₈×C₄₁	—	2	1	no	—
177	C₂×Q₈×C₄₁	—	2	1	no	—
178	C₂×Q₈×C₄₁	—	2	1	no	—
179	C₂×Q₈×C₄₁	—	2	1	no	—
180	C₂×Q₈×C₄₁	—	2	1	no	—
181	C₂×Q₈×C₄₁	—	2	1	no	—
182	C₂×Q₈×C₄₁	—	2	1	no	—
183	C₂×Q₈×C₄₁	—	2	1	no	—
184	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
185	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
186	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
187	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₄₁	—	2	2	no	—
189	C₂×D₄×C₄₁	—	2	2	no	—
190	C₂×D₄×C₄₁	—	2	2	no	—
191	C₂×D₄×C₄₁	—	2	2	no	—
192	C₂×D₄×C₄₁	—	2	2	no	—
193	C₂×D₄×C₄₁	—	2	2	no	—
194	C₂×D₄×C₄₁	—	2	2	no	—
195	C₂×D₄×C₄₁	—	2	2	no	—
196	C₂×D₄×C₄₁	—	2	1	no	—
197	C₂×D₄×C₄₁	—	2	1	no	—
198	C₂×D₄×C₄₁	—	2	1	no	—
199	C₂×D₄×C₄₁	—	2	1	no	—
200	C₂×D₄×C₄₁	—	2	1	no	—
201	C₂×D₄×C₄₁	—	2	1	no	—
202	C₂×D₄×C₄₁	—	2	1	no	—
203	C₂×D₄×C₄₁	—	2	1	no	—
204	C₂×D₄×C₄₁	—	4	1	no	—
205	C₂×D₄×C₄₁	—	4	1	no	—
206	C₂×D₄×C₄₁	—	4	1	no	—
207	C₂×D₄×C₄₁	—	4	1	no	—
208	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
209	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
210	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
211	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
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	2	no	—
216	C₂²×C₄×C₄₁	—	2	2	no	—
217	C₂²×C₄×C₄₁	—	2	2	no	—
218	C₂²×C₄×C₄₁	—	2	2	no	—
219	C₂²×C₄×C₄₁	—	2	1	no	—
220	C₂²×C₄×C₄₁	—	2	8	no	—
221	C₂²×C₄×C₄₁	—	2	2	no	—
222	C₂²×C₄×C₄₁	—	2	2	no	—
223	C₂²×C₄×C₄₁	—	2	2	no	—
224	C₂²×C₄×C₄₁	—	2	2	no	—
225	C₂²×C₄×C₄₁	—	4	1	no	—
226	C₂²×C₄×C₄₁	—	4	1	no	—
227	C₂²×C₄×C₄₁	—	4	1	no	—
228	C₂²×C₄×C₄₁	—	4	1	no	—
229	C₂²×C₄×C₄₁	—	4	1	no	—
230	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
240	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
241	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
242	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
243	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
244	Q₁₆×C₄₁	—	2	8	no	—
245	SD₁₆×C₄₁	—	2	8	no	—
246	SD₁₆×C₄₁	—	2	8	no	—
247	D₈×C₄₁	—	2	8	no	—
248	M₁₆×C₄₁	—	2	2	no	—
249	M₁₆×C₄₁	—	2	2	no	—
250	M₁₆×C₄₁	—	2	2	no	—
251	M₁₆×C₄₁	—	2	2	no	—
252	M₁₆×C₄₁	—	2	2	no	—
253	M₁₆×C₄₁	—	4	1	no	—
254	M₁₆×C₄₁	—	4	1	no	—
255	M₁₆×C₄₁	C₂²×C₄	1	4	yes	—
256	C₂×C₈×C₄₁	—	2	2	no	—
257	C₂×C₈×C₄₁	—	2	2	no	—
258	C₂×C₈×C₄₁	—	2	2	no	—
259	C₂×C₈×C₄₁	—	2	2	no	—
260	C₂×C₈×C₄₁	—	4	1	no	—
261	C₂×C₈×C₄₁	—	4	1	no	—
262	C₄⋊C₄×C₄₁	—	2	8	no	—
263	C₄⋊C₄×C₄₁	—	2	2	no	—
264	C₄⋊C₄×C₄₁	—	2	2	no	—
265	C₄⋊C₄×C₄₁	—	2	2	no	—
266	C₄⋊C₄×C₄₁	—	2	2	no	—
267	C₄⋊C₄×C₄₁	—	2	2	no	—
268	C₄⋊C₄×C₄₁	—	4	1	no	—
269	C₂²⋊C₄×C₄₁	—	2	8	no	—
270	C₂²⋊C₄×C₄₁	—	2	2	no	—
271	C₂²⋊C₄×C₄₁	—	2	2	no	—
272	C₂²⋊C₄×C₄₁	—	2	2	no	—
273	C₂²⋊C₄×C₄₁	—	2	2	no	—
274	C₂²⋊C₄×C₄₁	—	4	1	no	—
275	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
276	C₄²×C₄₁	—	2	8	no	—
277	C₄²×C₄₁	—	2	2	no	—
278	C₄²×C₄₁	—	2	2	no	—
279	C₄²×C₄₁	—	2	2	no	—
280	C₄²×C₄₁	—	2	2	no	—
281	C₄²×C₄₁	—	4	1	no	—
282	C₄²×C₄₁	C₂×D₄	1	4	yes	—
283	C₂³×C₄₁	—	2	2	no	—
284	C₂³×C₄₁	—	2	2	no	—
285	C₂³×C₄₁	—	2	2	no	—
286	C₂³×C₄₁	—	2	2	no	—
287	C₂³×C₄₁	—	4	1	no	—
288	C₂³×C₄₁	—	4	1	no	—
289	C₂³×C₄₁	—	8	1	no	—
290	C₂³×C₄₁	—	8	2	no	—
291	C₂³×C₄₁	—	8	2	no	—
292	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
293	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
294	C₂³×C₄₁	#120	1	1	yes	characteristic
295	C₂³×C₄₁	#120	1	1	yes	characteristic
296	C₂³×C₄₁	#121	1	1	yes	characteristic
297	C₂³×C₄₁	#121	1	1	yes	characteristic
298	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
299	Q₈×C₄₁	—	2	2	no	—
300	Q₈×C₄₁	—	2	2	no	—
301	Q₈×C₄₁	—	2	2	no	—
302	Q₈×C₄₁	—	2	2	no	—
303	Q₈×C₄₁	—	2	2	no	—
304	Q₈×C₄₁	—	4	1	no	—
305	Q₈×C₄₁	—	4	1	no	—
306	Q₈×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
307	D₄×C₄₁	—	2	4	no	—
308	D₄×C₄₁	—	2	4	no	—
309	D₄×C₄₁	—	2	4	no	—
310	D₄×C₄₁	—	2	4	no	—
311	D₄×C₄₁	—	2	2	no	—
312	D₄×C₄₁	—	2	2	no	—
313	D₄×C₄₁	—	2	2	no	—
314	D₄×C₄₁	—	2	2	no	—
315	D₄×C₄₁	—	2	2	no	—
316	D₄×C₄₁	—	4	2	no	—
317	D₄×C₄₁	—	4	2	no	—
318	D₄×C₄₁	—	4	2	no	—
319	D₄×C₄₁	—	4	2	no	—
320	D₄×C₄₁	—	4	1	no	—
321	D₄×C₄₁	—	4	1	no	—
322	D₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
323	C₂×C₄×C₄₁	—	2	2	no	—
324	C₂×C₄×C₄₁	—	2	2	no	—
325	C₂×C₄×C₄₁	—	2	2	no	—
326	C₂×C₄×C₄₁	—	2	4	no	—
327	C₂×C₄×C₄₁	—	2	4	no	—
328	C₂×C₄×C₄₁	—	2	4	no	—
329	C₂×C₄×C₄₁	—	2	4	no	—
330	C₂×C₄×C₄₁	—	2	2	no	—
331	C₂×C₄×C₄₁	—	2	4	no	—
332	C₂×C₄×C₄₁	—	2	4	no	—
333	C₂×C₄×C₄₁	—	4	1	no	—
334	C₂×C₄×C₄₁	—	4	1	no	—
335	C₂×C₄×C₄₁	—	4	2	no	—
336	C₂×C₄×C₄₁	—	4	2	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	—	8	2	no	—
341	C₂×C₄×C₄₁	—	8	2	no	—
342	C₂×C₄×C₄₁	—	8	8	no	—
343	C₂×C₄×C₄₁	—	8	2	no	—
344	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
349	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
350	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
351	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
352	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
353	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
354	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
355	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
356	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
357	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
358	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
359	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
360	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
361	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
362	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
363	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
364	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
365	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
366	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
372	C₈×C₄₁	—	2	4	no	—
373	C₈×C₄₁	—	4	2	no	—
374	#21000	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂²×C₄₁	—	2	4	no	—
376	C₂²×C₄₁	—	4	1	no	—
377	C₂²×C₄₁	—	4	1	no	—
378	C₂²×C₄₁	—	4	1	no	—
379	C₂²×C₄₁	—	4	1	no	—
380	C₂²×C₄₁	—	4	1	no	—
381	C₂²×C₄₁	—	4	1	no	—
382	C₂²×C₄₁	—	4	1	no	—
383	C₂²×C₄₁	—	4	4	no	—
384	C₂²×C₄₁	—	4	2	no	—
385	C₂²×C₄₁	—	8	2	no	—
386	C₂²×C₄₁	—	8	2	no	—
387	C₂²×C₄₁	—	8	2	no	—
388	C₂²×C₄₁	—	8	2	no	—
389	C₂²×C₄₁	—	8	2	no	—
390	C₂²×C₄₁	#386	1	1	yes	characteristic
391	C₂²×C₄₁	#386	1	1	yes	characteristic
392	C₂²×C₄₁	#386	1	1	yes	characteristic
393	C₂²×C₄₁	#386	1	1	yes	characteristic
394	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
395	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
396	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
397	C₄×C₄₁	—	2	4	no	—
398	C₄×C₄₁	—	4	4	no	—
399	C₄×C₄₁	—	4	4	no	—
400	C₄×C₄₁	—	4	2	no	—
401	C₄×C₄₁	—	8	2	no	—
402	C₄×C₄₁	#386	1	1	yes	characteristic
403	C₄×C₄₁	#386	1	1	yes	characteristic
404	C₄×C₄₁	#386	1	1	yes	characteristic
405	C₄×C₄₁	#386	1	1	yes	characteristic
406	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
407	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
408	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
409	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
410	C₂×#575	C₂×C₄₁	1	1	yes	characteristic
411	#3428	C₂×C₄₁	1	1	yes	characteristic, complemented
412	C₂×#421	C₂×C₄₁	1	1	yes	characteristic, complemented
413	C₂×#421	C₂×C₄₁	1	1	yes	characteristic, complemented
414	C₂×#410	C₂×C₄₁	1	1	yes	characteristic, complemented
415	#1906	C₂×C₄₁	1	8	yes	complemented
416	C₂×#344	C₂×C₄₁	1	1	yes	characteristic, complemented
417	#1733	C₂×C₄₁	1	1	yes	characteristic, complemented
418	C₂×C₄₁	—	2	1	no	—
419	C₂×C₄₁	—	2	1	no	—
420	C₂×C₄₁	—	2	1	no	—
421	C₂×C₄₁	—	2	1	no	—
422	C₂×C₄₁	—	2	1	no	—
423	C₂×C₄₁	—	2	1	no	—
424	C₂×C₄₁	—	2	1	no	—
425	C₂×C₄₁	—	4	4	no	—
426	C₂×C₄₁	—	8	2	no	—
427	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
428	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
429	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
430	#575	—	2	2	no	—
431	#575	—	2	2	no	—
432	#575	C₄×C₄₁	1	4	yes	complemented
433	#575	C₂²×C₄₁	1	4	yes	—
434	C₂×#137	—	2	1	no	—
435	C₂×#137	C₄×C₄₁	1	2	yes	complemented
436	C₂×AGL(1,ℤ/8)	—	2	1	no	—
437	C₂×AGL(1,ℤ/8)	C₄×C₄₁	1	2	yes	complemented
438	C₂×#135	—	2	2	no	—
439	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
440	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
441	#520	—	2	2	no	—
442	#520	—	2	2	no	—
443	#519	—	2	1	no	—
444	#518	—	2	1	no	—
445	#518	—	2	2	no	—
446	C₄×#41	—	2	2	no	—
447	C₄×#41	C₂²×C₄₁	1	4	yes	complemented
448	C₂×#117	—	2	2	no	—
449	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
450	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
451	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
452	#421	—	2	2	no	—
453	#421	—	2	2	no	—
454	#421	—	2	2	no	—
455	#421	C₂²×C₄₁	1	4	yes	complemented
456	C₂×#104	—	2	2	no	—
457	C₂×#104	C₂²×C₄₁	1	4	yes	complemented
458	#410	—	2	2	no	—
459	#410	C₂²×C₄₁	1	4	yes	complemented
460	C₂×#99	—	2	2	no	—
461	#344	C₂²×C₄₁	1	4	yes	complemented
462	#339	C₂²×C₄₁	1	4	yes	complemented
463	C₄₁	#21000	1	1	yes	characteristic, direct product factor, Sylow
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	1	no	—
468	C₂×#41	—	2	1	no	—
469	C₂×#41	—	2	1	no	—
470	C₂×#41	—	2	1	no	—
471	C₂×#41	—	2	1	no	—
472	C₂×#41	—	2	1	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	—	2	1	no	—
475	C₂×#41	—	2	1	no	—
476	C₂×#41	—	2	1	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	1	no	—
480	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
481	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
482	C₂×#41	C₂×C₄×C₄₁	1	2	yes	complemented
483	C₂×#41	D₄×C₄₁	1	2	yes	—
484	C₂×#41	D₄×C₄₁	1	2	yes	—
485	C₂×#41	D₄×C₄₁	1	2	yes	—
486	C₂×#41	C₂³×C₄₁	1	2	yes	—
487	C₂×#41	C₂³×C₄₁	1	2	yes	—
488	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
489	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
493	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
497	#137	—	2	4	no	—
498	#137	—	2	4	no	—
499	#137	—	2	4	no	—
500	#137	C₂×C₄×C₄₁	1	8	yes	complemented
501	AGL(1,ℤ/8)	—	2	4	no	—
502	AGL(1,ℤ/8)	—	2	4	no	—
503	AGL(1,ℤ/8)	—	2	4	no	—
504	AGL(1,ℤ/8)	C₂×C₄×C₄₁	1	8	yes	complemented
505	#135	—	2	8	no	—
506	#135	—	2	8	no	—
507	C₂×Q₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	2	no	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×D₈	—	2	2	no	—
511	C₂×M₁₆	—	2	1	no	—
512	C₂×M₁₆	—	2	1	no	—
513	C₂×M₁₆	—	2	1	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	1	no	—
516	C₂×M₁₆	—	2	1	no	—
517	C₂×M₁₆	—	2	1	no	—
518	C₂×M₁₆	—	2	1	no	—
519	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	complemented
520	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	complemented
521	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
522	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
523	C₂²×C₈	—	2	1	no	—
524	C₂²×C₈	—	2	1	no	—
525	C₄×Q₈	—	2	4	no	—
526	C₄×Q₈	—	2	4	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	4	no	—
529	C₄×D₄	—	2	4	no	—
530	C₄×D₄	—	2	8	no	—
531	#117	—	2	4	no	—
532	#117	—	2	4	no	—
533	#117	—	2	1	no	—
534	#117	—	2	1	no	—
535	#117	—	2	1	no	—
536	#117	—	2	1	no	—
537	#117	—	2	1	no	—
538	#117	—	2	4	no	—
539	#117	—	2	1	no	—
540	#117	—	2	1	no	—
541	#117	D₄×C₄₁	1	2	yes	—
542	#117	D₄×C₄₁	1	2	yes	—
543	#117	D₄×C₄₁	1	2	yes	—
544	#117	C₂³×C₄₁	1	2	yes	—
545	#117	C₂³×C₄₁	1	2	yes	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	4	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
554	C₂×C₄²	—	2	1	no	—
555	C₂×C₄²	—	2	4	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
558	#104	—	2	8	no	—
559	#104	—	2	8	no	—
560	#99	—	2	8	no	—
561	C₂⁴	—	2	1	no	—
562	C₂⁴	—	2	1	no	—
563	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
564	#41	—	2	2	no	—
565	#41	—	2	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	2	2	no	—
569	#41	—	2	2	no	—
570	#41	—	2	2	no	—
571	#41	—	2	2	no	—
572	#41	—	2	2	no	—
573	#41	—	2	2	no	—
574	#41	—	2	2	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	2	no	—
578	#41	—	2	2	no	—
579	#41	—	2	2	no	—
580	#41	—	2	2	no	—
581	#41	—	2	2	no	—
582	#41	—	2	2	no	—
583	#41	—	2	2	no	—
584	#41	—	4	1	no	—
585	#41	—	4	1	no	—
586	#41	—	4	1	no	—
587	#41	—	4	1	no	—
588	#41	—	4	1	no	—
589	#41	—	4	1	no	—
590	#41	—	4	1	no	—
591	#41	—	4	1	no	—
592	#41	C₂²⋊C₄×C₄₁	1	4	yes	—
593	#41	C₂²⋊C₄×C₄₁	1	4	yes	—
594	#41	C₂²×C₄×C₄₁	1	4	yes	—
595	#41	C₂×D₄×C₄₁	1	4	yes	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
605	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
606	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
607	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	4	1	no	—
625	C₂×D₄	—	4	1	no	—
626	C₂×D₄	—	4	1	no	—
627	C₂×D₄	—	4	1	no	—
628	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
629	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
630	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
631	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	4	1	no	—
646	C₂²×C₄	—	4	1	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
651	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
659	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
660	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
661	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
662	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
664	Q₁₆	—	2	8	no	—
665	SD₁₆	—	2	8	no	—
666	SD₁₆	—	2	8	no	—
667	D₈	—	2	8	no	—
668	M₁₆	—	2	2	no	—
669	M₁₆	—	2	2	no	—
670	M₁₆	—	2	2	no	—
671	M₁₆	—	2	2	no	—
672	M₁₆	—	2	2	no	—
673	M₁₆	—	4	1	no	—
674	M₁₆	—	4	1	no	—
675	M₁₆	C₂²×C₄×C₄₁	1	4	yes	—
676	C₂×C₈	—	2	2	no	—
677	C₂×C₈	—	2	2	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	4	1	no	—
681	C₂×C₈	—	4	1	no	—
682	C₄⋊C₄	—	2	8	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	4	1	no	—
689	C₂²⋊C₄	—	2	8	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
696	C₄²	—	2	8	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	4	1	no	—
702	C₄²	C₂×D₄×C₄₁	1	4	yes	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	8	1	no	—
710	C₂³	—	8	2	no	—
711	C₂³	—	8	2	no	—
712	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
713	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
714	C₂³	#120×C₄₁	1	1	yes	characteristic
715	C₂³	#120×C₄₁	1	1	yes	characteristic
716	C₂³	#121×C₄₁	1	1	yes	characteristic
717	C₂³	#121×C₄₁	1	1	yes	characteristic
718	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	4	1	no	—
725	Q₈	—	4	1	no	—
726	Q₈	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	4	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	2	no	—
732	D₄	—	2	2	no	—
733	D₄	—	2	2	no	—
734	D₄	—	2	2	no	—
735	D₄	—	2	2	no	—
736	D₄	—	4	2	no	—
737	D₄	—	4	2	no	—
738	D₄	—	4	2	no	—
739	D₄	—	4	2	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	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	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	8	2	no	—
761	C₂×C₄	—	8	2	no	—
762	C₂×C₄	—	8	8	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
765	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
766	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
767	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
768	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
769	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
770	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
771	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
772	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
773	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
774	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
775	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
776	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
777	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
778	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
779	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
780	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
781	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
782	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
783	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
784	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
785	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
786	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
790	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
791	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
792	C₈	—	2	4	no	—
793	C₈	—	4	2	no	—
794	C₂²	—	2	4	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	8	2	no	—
805	C₂²	—	8	2	no	—
806	C₂²	—	8	2	no	—
807	C₂²	—	8	2	no	—
808	C₂²	—	8	2	no	—
809	C₂²	C₄₁×#386	1	1	yes	characteristic
810	C₂²	C₄₁×#386	1	1	yes	characteristic
811	C₂²	C₄₁×#386	1	1	yes	characteristic
812	C₂²	C₄₁×#386	1	1	yes	characteristic
813	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
814	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
815	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
816	C₄	—	2	4	no	—
817	C₄	—	4	4	no	—
818	C₄	—	4	4	no	—
819	C₄	—	4	2	no	—
820	C₄	—	8	2	no	—
821	C₄	C₄₁×#386	1	1	yes	characteristic
822	C₄	C₄₁×#386	1	1	yes	characteristic
823	C₄	C₄₁×#386	1	1	yes	characteristic
824	C₄	C₄₁×#386	1	1	yes	characteristic
825	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
826	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
827	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
828	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
829	C₂	—	2	1	no	—
830	C₂	—	2	1	no	—
831	C₂	—	2	1	no	—
832	C₂	—	2	1	no	—
833	C₂	—	2	1	no	—
834	C₂	—	2	1	no	—
835	C₂	—	2	1	no	—
836	C₂	—	4	4	no	—
837	C₂	—	8	2	no	—
838	C₂	C₂×C₄₁×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂×C₄₁	C₂×#386
prime radical	C₂×C₄₁×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#3428	C₂	semidirect
3. C₂×C₄₁×#421	C₂	semidirect
4. C₂×C₄₁×#421	C₂	semidirect
5. C₂×C₄₁×#410	C₂	semidirect
6. C₄₁×#1906	C₂	semidirect
7. C₂×C₄₁×#344	C₂	semidirect
8. C₄₁×#1733	C₂	semidirect
13. C₄₁×#575	C₄	semidirect
16. C₂×#137×C₄₁	C₄	semidirect
18. C₂×AGL(1,ℤ/8)×C₄₁	C₄	semidirect
28. C₄×#41×C₄₁	C₂²	semidirect
36. C₄₁×#421	C₂²	semidirect
38. C₂×#104×C₄₁	C₂²	semidirect
40. C₄₁×#410	C₂²	semidirect
42. C₄₁×#344	C₂²	semidirect
43. C₄₁×#339	C₂²	semidirect
62. C₂×#41×C₄₁	C₂×C₄	semidirect
68. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
72. C₂²×D₄×C₄₁	C₂×C₄	semidirect
80. #137×C₄₁	C₂×C₄	semidirect
84. AGL(1,ℤ/8)×C₄₁	C₂×C₄	semidirect
99. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
100. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
374. #21000	C₄₁	direct (N × H)
411. #3428	C₂×C₄₁	semidirect
412. C₂×#421	C₂×C₄₁	semidirect
413. C₂×#421	C₂×C₄₁	semidirect
414. C₂×#410	C₂×C₄₁	semidirect
415. #1906	C₂×C₄₁	semidirect
416. C₂×#344	C₂×C₄₁	semidirect
417. #1733	C₂×C₄₁	semidirect
432. #575	C₄×C₄₁	semidirect
435. C₂×#137	C₄×C₄₁	semidirect
437. C₂×AGL(1,ℤ/8)	C₄×C₄₁	semidirect
447. C₄×#41	C₂²×C₄₁	semidirect
455. #421	C₂²×C₄₁	semidirect
457. C₂×#104	C₂²×C₄₁	semidirect
459. #410	C₂²×C₄₁	semidirect
461. #344	C₂²×C₄₁	semidirect
462. #339	C₂²×C₄₁	semidirect
463. C₄₁	#21000	direct (N × H)
482. C₂×#41	C₂×C₄×C₄₁	semidirect
488. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
492. C₂²×D₄	C₂×C₄×C₄₁	semidirect
500. #137	C₂×C₄×C₄₁	semidirect
504. AGL(1,ℤ/8)	C₂×C₄×C₄₁	semidirect
519. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
520. C₂×M₁₆	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#575	2
C₄₁×#3428	2
C₂×C₄₁×#421	2
C₂×C₄₁×#410	2
C₄₁×#1906	2
C₂×C₄₁×#344	2
C₄₁×#1733	2
#21000	41

Subgroups — C41×#21000 #23797201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21000 #23797201