Subgroups — C₄₁×#23933 #23800134

Order 10496.

1488 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#450	C₂	1	2	yes	maximal
3	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2023	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2013	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1880	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1872	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1817	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₄₁	C₂²	1	4	yes	—
11	C₄₁×#533	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
14	C₂×#125×C₄₁	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	complemented
19	C₂×#117×C₄₁	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
22	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
23	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#450	—	2	8	no	—
25	C₂×#103×C₄₁	C₂²	1	4	yes	complemented
26	C₂×#102×C₄₁	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#390	—	2	1	no	—
29	C₄₁×#390	—	2	1	no	—
30	C₄₁×#390	C₂²	1	2	yes	—
31	C₄₁×#390	C₂²	1	2	yes	—
32	C₄₁×#340	C₂²	1	4	yes	complemented
33	C₄₁×#336	C₂²	1	2	yes	complemented
34	C₄₁×#336	C₂²	1	2	yes	complemented
35	C₂⁵×C₄₁	—	2	1	no	—
36	C₂²×Q₈×C₄₁	—	2	1	no	—
37	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
38	C₂²×D₄×C₄₁	—	2	4	no	—
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	—	2	4	no	—
41	C₂²×D₄×C₄₁	—	4	2	no	—
42	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
47	C₂×SD₁₆×C₄₁	—	2	8	no	—
48	C₂×SD₁₆×C₄₁	—	2	8	no	—
49	C₂×SD₁₆×C₄₁	—	4	4	no	—
50	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
51	C₄⋊Q₈×C₄₁	—	2	4	no	—
52	C₄⋊Q₈×C₄₁	—	2	4	no	—
53	#125×C₄₁	—	2	8	no	—
54	C₂²⋊Q₈×C₄₁	—	2	8	no	—
55	C₂²⋊Q₈×C₄₁	—	2	4	no	—
56	C₂²⋊Q₈×C₄₁	D₄	1	8	yes	—
57	C₄×Q₈×C₄₁	—	2	8	no	—
58	C₄×Q₈×C₄₁	—	2	4	no	—
59	C₄×Q₈×C₄₁	—	2	4	no	—
60	#117×C₄₁	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
77	C₂×C₄²×C₄₁	—	2	4	no	—
78	C₂×C₄²×C₄₁	—	2	2	no	—
79	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
83	#103×C₄₁	—	4	4	no	—
84	#102×C₄₁	—	2	8	no	—
85	C₂²⋊C₈×C₄₁	—	2	4	no	—
86	C₂⁴×C₄₁	—	2	4	no	—
87	C₂⁴×C₄₁	—	2	2	no	—
88	C₂⁴×C₄₁	—	4	2	no	—
89	C₂⁴×C₄₁	—	4	2	no	—
90	C₂⁴×C₄₁	—	4	2	no	—
91	C₂⁴×C₄₁	—	4	2	no	—
92	C₂⁴×C₄₁	—	4	2	no	—
93	C₂⁴×C₄₁	—	4	2	no	—
94	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₁	—	2	4	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	4	no	—
98	C₂×Q₈×C₄₁	—	2	4	no	—
99	C₂×Q₈×C₄₁	—	4	2	no	—
100	C₂×Q₈×C₄₁	—	4	2	no	—
101	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
102	C₂×D₄×C₄₁	—	2	4	no	—
103	C₂×D₄×C₄₁	—	2	4	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	4	no	—
106	C₂×D₄×C₄₁	—	4	16	no	—
107	C₂×D₄×C₄₁	—	4	2	no	—
108	C₂×D₄×C₄₁	—	4	2	no	—
109	C₂×D₄×C₄₁	#41	1	4	yes	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	—	2	2	no	—
116	C₂²×C₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	2	2	no	—
119	C₂²×C₄×C₄₁	—	4	1	no	—
120	C₂²×C₄×C₄₁	—	4	2	no	—
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	—	4	2	no	—
123	C₂²×C₄×C₄₁	SD₁₆	1	4	yes	complemented
124	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
131	SD₁₆×C₄₁	—	4	16	no	—
132	C₂×C₈×C₄₁	—	2	4	no	—
133	C₂×C₈×C₄₁	—	2	4	no	—
134	C₂×C₈×C₄₁	—	2	4	no	—
135	C₄⋊C₄×C₄₁	—	2	4	no	—
136	C₄⋊C₄×C₄₁	—	2	4	no	—
137	C₄⋊C₄×C₄₁	—	2	8	no	—
138	C₄⋊C₄×C₄₁	—	2	4	no	—
139	C₄⋊C₄×C₄₁	—	2	8	no	—
140	C₄⋊C₄×C₄₁	—	2	2	no	—
141	C₄⋊C₄×C₄₁	—	2	4	no	—
142	C₄⋊C₄×C₄₁	—	4	2	no	—
143	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
144	C₂²⋊C₄×C₄₁	—	2	8	no	—
145	C₂²⋊C₄×C₄₁	—	4	4	no	—
146	C₂²⋊C₄×C₄₁	—	4	4	no	—
147	C₂²⋊C₄×C₄₁	—	4	4	no	—
148	C₂²⋊C₄×C₄₁	—	4	4	no	—
149	C₄²×C₄₁	—	2	8	no	—
150	C₄²×C₄₁	—	2	2	no	—
151	C₄²×C₄₁	—	2	2	no	—
152	C₄²×C₄₁	—	2	2	no	—
153	C₄²×C₄₁	—	2	2	no	—
154	C₂³×C₄₁	—	2	1	no	—
155	C₂³×C₄₁	—	2	1	no	—
156	C₂³×C₄₁	—	2	1	no	—
157	C₂³×C₄₁	—	2	1	no	—
158	C₂³×C₄₁	—	2	4	no	—
159	C₂³×C₄₁	—	4	8	no	—
160	C₂³×C₄₁	—	4	8	no	—
161	C₂³×C₄₁	—	4	8	no	—
162	C₂³×C₄₁	—	4	2	no	—
163	C₂³×C₄₁	—	4	2	no	—
164	C₂³×C₄₁	—	4	2	no	—
165	C₂³×C₄₁	—	4	2	no	—
166	C₂³×C₄₁	—	4	2	no	—
167	C₂³×C₄₁	—	4	2	no	—
168	C₂³×C₄₁	—	8	4	no	—
169	C₂³×C₄₁	—	8	4	no	—
170	C₂³×C₄₁	—	8	4	no	—
171	C₂³×C₄₁	—	8	4	no	—
172	C₂³×C₄₁	#120	1	2	yes	—
173	C₂³×C₄₁	C₂×SD₁₆	1	2	yes	—
174	C₂³×C₄₁	#137	1	2	yes	—
175	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₄₁	—	2	8	no	—
177	Q₈×C₄₁	—	4	8	no	—
178	Q₈×C₄₁	—	4	4	no	—
179	D₄×C₄₁	—	2	8	no	—
180	D₄×C₄₁	—	4	8	no	—
181	D₄×C₄₁	—	4	4	no	—
182	C₂×C₄×C₄₁	—	2	1	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	1	no	—
186	C₂×C₄×C₄₁	—	2	1	no	—
187	C₂×C₄×C₄₁	—	2	1	no	—
188	C₂×C₄×C₄₁	—	2	1	no	—
189	C₂×C₄×C₄₁	—	2	1	no	—
190	C₂×C₄×C₄₁	—	2	8	no	—
191	C₂×C₄×C₄₁	—	2	8	no	—
192	C₂×C₄×C₄₁	—	2	1	no	—
193	C₂×C₄×C₄₁	—	2	4	no	—
194	C₂×C₄×C₄₁	—	2	4	no	—
195	C₂×C₄×C₄₁	—	2	1	no	—
196	C₂×C₄×C₄₁	—	2	1	no	—
197	C₂×C₄×C₄₁	—	4	4	no	—
198	C₂×C₄×C₄₁	—	4	2	no	—
199	C₂×C₄×C₄₁	—	4	2	no	—
200	C₂×C₄×C₄₁	—	4	2	no	—
201	C₂×C₄×C₄₁	—	4	2	no	—
202	C₂×C₄×C₄₁	—	4	2	no	—
203	C₂×C₄×C₄₁	—	4	2	no	—
204	C₂×C₄×C₄₁	—	4	2	no	—
205	C₂×C₄×C₄₁	—	8	4	no	—
206	C₂×C₄×C₄₁	#120	1	2	yes	—
207	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
208	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
209	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
210	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
212	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
213	C₈×C₄₁	—	4	4	no	—
214	#23933	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₁	—	2	2	no	—
216	C₂²×C₄₁	—	2	2	no	—
217	C₂²×C₄₁	—	2	2	no	—
218	C₂²×C₄₁	—	2	2	no	—
219	C₂²×C₄₁	—	2	2	no	—
220	C₂²×C₄₁	—	2	2	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	—	4	4	no	—
223	C₂²×C₄₁	—	4	4	no	—
224	C₂²×C₄₁	—	8	16	no	—
225	C₂²×C₄₁	—	8	2	no	—
226	C₂²×C₄₁	—	8	2	no	—
227	C₂²×C₄₁	—	8	2	no	—
228	C₂²×C₄₁	—	8	2	no	—
229	C₂²×C₄₁	#448	1	4	yes	—
230	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
231	C₂²×C₄₁	#525	1	1	yes	characteristic
232	C₂²×C₄₁	#535	1	1	yes	characteristic
233	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
234	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
236	C₂²×C₄₁	#575	1	1	yes	characteristic
237	C₄×C₄₁	—	2	2	no	—
238	C₄×C₄₁	—	2	2	no	—
239	C₄×C₄₁	—	2	2	no	—
240	C₄×C₄₁	—	2	2	no	—
241	C₄×C₄₁	—	4	4	no	—
242	C₄×C₄₁	—	4	1	no	—
243	C₄×C₄₁	—	4	4	no	—
244	C₄×C₄₁	—	8	2	no	—
245	C₄×C₄₁	#546	1	4	yes	—
246	C₂×#533	C₂×C₄₁	1	1	yes	characteristic, complemented
247	C₂×#450	C₂×C₄₁	1	2	yes	—
248	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
249	#2023	C₂×C₄₁	1	2	yes	complemented
250	#2013	C₂×C₄₁	1	2	yes	complemented
251	#1880	C₂×C₄₁	1	4	yes	complemented
252	#1872	C₂×C₄₁	1	2	yes	complemented
253	#1817	C₂×C₄₁	1	1	yes	characteristic, complemented
254	C₂×C₄₁	—	2	4	no	—
255	C₂×C₄₁	—	8	4	no	—
256	C₂×C₄₁	#2404	1	1	yes	characteristic
257	C₂×C₄₁	C₂×#448	1	1	yes	characteristic
258	C₂×C₄₁	#3006	1	1	yes	characteristic
259	C₂×C₄₁	#3101	1	1	yes	characteristic
260	C₂×C₄₁	#3110	1	1	yes	characteristic
261	C₂×C₄₁	#3208	1	1	yes	characteristic
262	C₂×C₄₁	#3215	1	1	yes	characteristic
263	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
264	C₂²×SD₁₆	C₂²×C₄₁	1	4	yes	—
265	#533	—	2	8	no	—
266	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
267	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
268	C₂×#125	—	2	1	no	—
269	C₂×C₂²⋊Q₈	—	2	1	no	—
270	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
271	C₂×C₄×Q₈	—	2	1	no	—
272	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	complemented
273	C₂×#117	—	2	1	no	—
274	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	—	2	1	no	—
276	C₂²×C₂²⋊C₄	—	2	1	no	—
277	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
278	#450	—	2	8	no	—
279	C₂×#103	C₂²×C₄₁	1	4	yes	complemented
280	C₂×#102	C₂²×C₄₁	1	4	yes	—
281	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
282	#390	—	2	1	no	—
283	#390	—	2	1	no	—
284	#390	C₂²×C₄₁	1	2	yes	—
285	#390	C₂²×C₄₁	1	2	yes	—
286	#340	C₂²×C₄₁	1	4	yes	complemented
287	#336	C₂²×C₄₁	1	2	yes	complemented
288	#336	C₂²×C₄₁	1	2	yes	complemented
289	C₄₁	#23933	1	1	yes	characteristic, direct product factor, Sylow
290	C₂⁵	—	2	1	no	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
293	C₂²×D₄	—	2	4	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	4	no	—
296	C₂²×D₄	—	4	2	no	—
297	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
302	C₂×SD₁₆	—	2	8	no	—
303	C₂×SD₁₆	—	2	8	no	—
304	C₂×SD₁₆	—	4	4	no	—
305	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
306	C₄⋊Q₈	—	2	4	no	—
307	C₄⋊Q₈	—	2	4	no	—
308	#125	—	2	8	no	—
309	C₂²⋊Q₈	—	2	8	no	—
310	C₂²⋊Q₈	—	2	4	no	—
311	C₂²⋊Q₈	D₄×C₄₁	1	8	yes	—
312	C₄×Q₈	—	2	8	no	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	—	2	4	no	—
315	#117	—	2	8	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	4	2	no	—
323	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	4	4	no	—
331	C₂×C₂²⋊C₄	—	4	4	no	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
335	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
338	#103	—	4	4	no	—
339	#102	—	2	8	no	—
340	C₂²⋊C₈	—	2	4	no	—
341	C₂⁴	—	2	4	no	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	—	4	2	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	4	2	no	—
346	C₂⁴	—	4	2	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	—	4	2	no	—
349	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	4	16	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	#41×C₄₁	1	4	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	SD₁₆×C₄₁	1	4	yes	complemented
379	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
382	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
386	SD₁₆	—	4	16	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	4	4	no	—
404	C₄²	—	2	8	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	4	8	no	—
416	C₂³	—	4	8	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	8	4	no	—
424	C₂³	—	8	4	no	—
425	C₂³	—	8	4	no	—
426	C₂³	—	8	4	no	—
427	C₂³	#120×C₄₁	1	2	yes	—
428	C₂³	C₂×SD₁₆×C₄₁	1	2	yes	—
429	C₂³	#137×C₄₁	1	2	yes	—
430	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
431	Q₈	—	2	8	no	—
432	Q₈	—	4	8	no	—
433	Q₈	—	4	4	no	—
434	D₄	—	2	8	no	—
435	D₄	—	4	8	no	—
436	D₄	—	4	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	#120×C₄₁	1	2	yes	—
462	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
463	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
464	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
466	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
467	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
468	C₈	—	4	4	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	8	16	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	—	8	2	no	—
482	C₂²	—	8	2	no	—
483	C₂²	C₄₁×#448	1	4	yes	—
484	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
485	C₂²	C₄₁×#525	1	1	yes	characteristic
486	C₂²	C₄₁×#535	1	1	yes	characteristic
487	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
488	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
489	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
490	C₂²	C₄₁×#575	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	4	no	—
498	C₄	—	8	2	no	—
499	C₄	C₄₁×#546	1	4	yes	—
500	C₂	—	2	4	no	—
501	C₂	—	8	4	no	—
502	C₂	C₄₁×#2404	1	1	yes	characteristic
503	C₂	C₂×C₄₁×#448	1	1	yes	characteristic
504	C₂	C₄₁×#3006	1	1	yes	characteristic
505	C₂	C₄₁×#3101	1	1	yes	characteristic
506	C₂	C₄₁×#3110	1	1	yes	characteristic
507	C₂	C₄₁×#3208	1	1	yes	characteristic
508	C₂	C₄₁×#3215	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#533	C₂	semidirect
4. C₄₁×#2023	C₂	semidirect
5. C₄₁×#2013	C₂	semidirect
6. C₄₁×#1880	C₂	semidirect
7. C₄₁×#1872	C₂	semidirect
8. C₄₁×#1817	C₂	semidirect
12. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
13. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
18. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
25. C₂×#103×C₄₁	C₂²	semidirect
32. C₄₁×#340	C₂²	semidirect
33. C₄₁×#336	C₂²	semidirect
34. C₄₁×#336	C₂²	semidirect
123. C₂²×C₄×C₄₁	SD₁₆	semidirect
214. #23933	C₄₁	direct (N × H)
246. C₂×#533	C₂×C₄₁	semidirect
249. #2023	C₂×C₄₁	semidirect
250. #2013	C₂×C₄₁	semidirect
251. #1880	C₂×C₄₁	semidirect
252. #1872	C₂×C₄₁	semidirect
253. #1817	C₂×C₄₁	semidirect
266. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
267. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
272. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
279. C₂×#103	C₂²×C₄₁	semidirect
286. #340	C₂²×C₄₁	semidirect
287. #336	C₂²×C₄₁	semidirect
288. #336	C₂²×C₄₁	semidirect
289. C₄₁	#23933	direct (N × H)
378. C₂²×C₄	SD₁₆×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×#533	2
C₂×C₄₁×#450	2
C₂×C₄₁×#390	2
C₄₁×#2023	2
C₄₁×#2013	2
C₄₁×#1880	2
C₄₁×#1872	2
C₄₁×#1817	2
#23933	41

Subgroups — C41×#23933 #23800134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23933 #23800134