Subgroups — C₂×C₄₁×#2431 #23810912

Order 10496.

6278 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#127×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#124×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#121×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2431	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₁×#392	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₁×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#386	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₄₁	—	2	8	no	—
12	C₂²×#41×C₄₁	—	2	8	no	—
13	C₂²×#41×C₄₁	—	2	8	no	—
14	C₂²×#41×C₄₁	C₂²	1	8	yes	complemented
15	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
17	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₄₁	C₂²	1	4	yes	—
19	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
21	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#127×C₄₁	—	2	8	no	—
24	C₂×#127×C₄₁	C₂²	1	8	yes	complemented
25	C₂×#124×C₄₁	—	2	8	no	—
26	C₂×#124×C₄₁	C₂²	1	8	yes	complemented
27	C₂×#121×C₄₁	—	2	8	no	—
28	C₂×#121×C₄₁	C₂²	1	8	yes	complemented
29	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
33	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
34	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#392	C₂²	1	32	yes	complemented
37	C₄₁×#391	C₂²	1	8	yes	complemented
38	C₄₁×#390	C₂²	1	8	yes	complemented
39	C₄₁×#386	C₂²	1	32	yes	complemented
40	C₄×C₂²⋊C₄×C₄₁	C₂²	1	8	yes	complemented
41	C₂×#95×C₄₁	C₂²	1	2	yes	—
42	C₂×#95×C₄₁	C₂²	1	4	yes	—
43	C₂⁵×C₄₁	C₂³	1	2	yes	—
44	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
45	C₂⁵×C₄₁	C₂³	1	2	yes	—
46	C₂×#41×C₄₁	—	2	128	no	—
47	C₂×#41×C₄₁	—	2	32	no	—
48	C₂×#41×C₄₁	—	2	32	no	—
49	C₂×#41×C₄₁	—	2	32	no	—
50	C₂²×Q₈×C₄₁	—	2	4	no	—
51	C₂²×Q₈×C₄₁	—	2	4	no	—
52	C₂²×Q₈×C₄₁	D₄	1	8	yes	complemented
53	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
54	C₂²×D₄×C₄₁	—	2	8	no	—
55	C₂²×D₄×C₄₁	—	2	8	no	—
56	C₂²×D₄×C₄₁	—	2	8	no	—
57	C₂²×D₄×C₄₁	—	2	16	no	—
58	C₂²×D₄×C₄₁	—	2	8	no	—
59	C₂²×D₄×C₄₁	—	2	4	no	—
60	C₂²×D₄×C₄₁	—	2	4	no	—
61	C₂²×D₄×C₄₁	—	2	4	no	—
62	C₂²×D₄×C₄₁	—	2	4	no	—
63	C₂²×D₄×C₄₁	—	2	4	no	—
64	C₂²×D₄×C₄₁	—	2	16	no	—
65	C₂²×D₄×C₄₁	—	4	8	no	—
66	C₂²×D₄×C₄₁	—	4	8	no	—
67	C₂²×D₄×C₄₁	D₄	1	8	yes	complemented
68	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
69	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
70	C₂²×D₄×C₄₁	C₂³	1	16	yes	—
71	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
72	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
73	C₂³×C₄×C₄₁	—	2	8	no	—
74	C₂³×C₄×C₄₁	—	2	8	no	—
75	C₂³×C₄×C₄₁	—	2	8	no	—
76	C₂³×C₄×C₄₁	—	2	4	no	—
77	C₂³×C₄×C₄₁	—	2	4	no	—
78	C₂³×C₄×C₄₁	D₄	1	8	yes	complemented
79	C₂³×C₄×C₄₁	C₂³	1	8	yes	—
80	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
85	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
86	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
87	#127×C₄₁	—	2	32	no	—
88	#124×C₄₁	—	2	32	no	—
89	#121×C₄₁	—	2	32	no	—
90	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
91	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	4	8	no	—
96	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
98	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	—
100	C₂×C₄²×C₄₁	—	2	4	no	—
101	C₂×C₄²×C₄₁	—	2	4	no	—
102	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
103	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
104	#95×C₄₁	C₂³	1	8	yes	—
105	#95×C₄₁	C₂³	1	16	yes	—
106	C₂⁴×C₄₁	—	2	4	no	—
107	C₂⁴×C₄₁	—	2	2	no	—
108	C₂⁴×C₄₁	—	2	4	no	—
109	C₂⁴×C₄₁	—	2	2	no	—
110	C₂⁴×C₄₁	—	2	4	no	—
111	C₂⁴×C₄₁	—	2	8	no	—
112	C₂⁴×C₄₁	—	2	8	no	—
113	C₂⁴×C₄₁	—	2	4	no	—
114	C₂⁴×C₄₁	—	2	4	no	—
115	C₂⁴×C₄₁	—	2	4	no	—
116	C₂⁴×C₄₁	—	2	4	no	—
117	C₂⁴×C₄₁	—	2	8	no	—
118	C₂⁴×C₄₁	—	2	8	no	—
119	C₂⁴×C₄₁	C₂×D₄	1	8	yes	—
120	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
121	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
122	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
123	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
124	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
125	#41×C₄₁	—	2	256	no	—
126	C₂×Q₈×C₄₁	—	2	32	no	—
127	C₂×Q₈×C₄₁	—	2	8	no	—
128	C₂×Q₈×C₄₁	—	2	8	no	—
129	C₂×Q₈×C₄₁	C₂×D₄	1	16	yes	complemented
130	C₂×D₄×C₄₁	—	2	64	no	—
131	C₂×D₄×C₄₁	—	2	16	no	—
132	C₂×D₄×C₄₁	—	2	16	no	—
133	C₂×D₄×C₄₁	—	2	16	no	—
134	C₂×D₄×C₄₁	—	2	32	no	—
135	C₂×D₄×C₄₁	—	2	32	no	—
136	C₂×D₄×C₄₁	—	2	16	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	—	2	8	no	—
141	C₂×D₄×C₄₁	—	2	8	no	—
142	C₂×D₄×C₄₁	—	2	32	no	—
143	C₂×D₄×C₄₁	—	4	16	no	—
144	C₂×D₄×C₄₁	—	4	16	no	—
145	C₂×D₄×C₄₁	—	4	64	no	—
146	C₂×D₄×C₄₁	—	4	32	no	—
147	C₂×D₄×C₄₁	—	4	16	no	—
148	C₂×D₄×C₄₁	C₂×D₄	1	16	yes	complemented
149	C₂²×C₄×C₄₁	—	2	64	no	—
150	C₂²×C₄×C₄₁	—	2	4	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	2	no	—
153	C₂²×C₄×C₄₁	—	2	4	no	—
154	C₂²×C₄×C₄₁	—	2	4	no	—
155	C₂²×C₄×C₄₁	—	2	16	no	—
156	C₂²×C₄×C₄₁	—	2	4	no	—
157	C₂²×C₄×C₄₁	—	2	32	no	—
158	C₂²×C₄×C₄₁	—	2	16	no	—
159	C₂²×C₄×C₄₁	—	2	16	no	—
160	C₂²×C₄×C₄₁	—	2	8	no	—
161	C₂²×C₄×C₄₁	—	2	8	no	—
162	C₂²×C₄×C₄₁	—	2	4	no	—
163	C₂²×C₄×C₄₁	—	2	4	no	—
164	C₂²×C₄×C₄₁	—	2	4	no	—
165	C₂²×C₄×C₄₁	—	2	4	no	—
166	C₂²×C₄×C₄₁	—	2	8	no	—
167	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₄₁	C₂×D₄	1	8	yes	—
169	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₄₁	C₂×D₄	1	16	yes	complemented
173	C₂²×C₄×C₄₁	#41	1	8	yes	complemented
174	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
180	C₄⋊C₄×C₄₁	—	2	8	no	—
181	C₂²⋊C₄×C₄₁	—	2	16	no	—
182	C₂²⋊C₄×C₄₁	—	2	32	no	—
183	C₂²⋊C₄×C₄₁	—	2	16	no	—
184	C₂²⋊C₄×C₄₁	—	4	16	no	—
185	C₄²×C₄₁	—	2	8	no	—
186	C₄²×C₄₁	—	2	8	no	—
187	C₂³×C₄₁	—	2	16	no	—
188	C₂³×C₄₁	—	2	8	no	—
189	C₂³×C₄₁	—	2	8	no	—
190	C₂³×C₄₁	—	2	8	no	—
191	C₂³×C₄₁	—	2	32	no	—
192	C₂³×C₄₁	—	2	4	no	—
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	—	2	4	no	—
195	C₂³×C₄₁	—	2	2	no	—
196	C₂³×C₄₁	—	2	4	no	—
197	C₂³×C₄₁	—	2	8	no	—
198	C₂³×C₄₁	—	2	8	no	—
199	C₂³×C₄₁	—	2	4	no	—
200	C₂³×C₄₁	—	2	4	no	—
201	C₂³×C₄₁	—	2	4	no	—
202	C₂³×C₄₁	—	2	4	no	—
203	C₂³×C₄₁	—	2	8	no	—
204	C₂³×C₄₁	—	2	8	no	—
205	C₂³×C₄₁	—	4	8	no	—
206	C₂³×C₄₁	—	4	8	no	—
207	C₂³×C₄₁	—	4	8	no	—
208	C₂³×C₄₁	—	4	8	no	—
209	C₂³×C₄₁	—	4	16	no	—
210	C₂³×C₄₁	—	4	8	no	—
211	C₂³×C₄₁	—	4	8	no	—
212	C₂³×C₄₁	—	4	8	no	—
213	C₂³×C₄₁	—	4	16	no	—
214	C₂³×C₄₁	—	4	16	no	—
215	C₂³×C₄₁	C₂²×D₄	1	8	yes	—
216	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
217	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
218	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
219	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
220	C₂³×C₄₁	C₂×#41	1	4	yes	—
221	C₂³×C₄₁	H(5,𝔽₂)	1	4	yes	—
222	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
223	Q₈×C₄₁	—	2	32	no	—
224	D₄×C₄₁	—	2	64	no	—
225	D₄×C₄₁	—	2	32	no	—
226	D₄×C₄₁	—	4	64	no	—
227	D₄×C₄₁	—	4	32	no	—
228	D₄×C₄₁	—	4	16	no	—
229	C₂×C₄×C₄₁	—	2	64	no	—
230	C₂×C₄×C₄₁	—	2	8	no	—
231	C₂×C₄×C₄₁	—	2	16	no	—
232	C₂×C₄×C₄₁	—	2	16	no	—
233	C₂×C₄×C₄₁	—	2	4	no	—
234	C₂×C₄×C₄₁	—	2	2	no	—
235	C₂×C₄×C₄₁	—	2	2	no	—
236	C₂×C₄×C₄₁	—	2	4	no	—
237	C₂×C₄×C₄₁	—	2	4	no	—
238	C₂×C₄×C₄₁	—	2	4	no	—
239	C₂×C₄×C₄₁	—	2	32	no	—
240	C₂×C₄×C₄₁	—	2	4	no	—
241	C₂×C₄×C₄₁	—	2	4	no	—
242	C₂×C₄×C₄₁	—	2	4	no	—
243	C₂×C₄×C₄₁	—	2	4	no	—
244	C₂×C₄×C₄₁	—	2	8	no	—
245	C₂×C₄×C₄₁	—	4	8	no	—
246	C₂×C₄×C₄₁	—	4	8	no	—
247	C₂×C₄×C₄₁	#120	1	16	yes	—
248	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
250	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
252	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₄₁	C₂×#41	1	8	yes	complemented
254	C₂×#2431	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₄₁	—	2	8	no	—
256	C₂²×C₄₁	—	2	4	no	—
257	C₂²×C₄₁	—	2	4	no	—
258	C₂²×C₄₁	—	2	4	no	—
259	C₂²×C₄₁	—	2	16	no	—
260	C₂²×C₄₁	—	4	4	no	—
261	C₂²×C₄₁	—	4	4	no	—
262	C₂²×C₄₁	—	4	16	no	—
263	C₂²×C₄₁	—	4	32	no	—
264	C₂²×C₄₁	—	4	4	no	—
265	C₂²×C₄₁	—	4	4	no	—
266	C₂²×C₄₁	—	4	8	no	—
267	C₂²×C₄₁	—	4	4	no	—
268	C₂²×C₄₁	—	4	4	no	—
269	C₂²×C₄₁	—	4	4	no	—
270	C₂²×C₄₁	—	4	8	no	—
271	C₂²×C₄₁	—	4	8	no	—
272	C₂²×C₄₁	—	8	16	no	—
273	C₂²×C₄₁	C₂×#120	1	4	yes	—
274	C₂²×C₄₁	#532	1	4	yes	—
275	C₂²×C₄₁	#535	1	4	yes	—
276	C₂²×C₄₁	#546	1	8	yes	—
277	C₂²×C₄₁	#550	1	8	yes	—
278	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
279	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
280	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
281	C₂²×C₄₁	C₂²×#41	1	2	yes	—
282	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
283	C₄×C₄₁	—	2	4	no	—
284	C₄×C₄₁	—	2	8	no	—
285	C₄×C₄₁	—	2	8	no	—
286	C₄×C₄₁	—	4	4	no	—
287	C₄×C₄₁	—	4	4	no	—
288	C₄×C₄₁	C₂×#120	1	8	yes	—
289	C₂³×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
290	C₂²×#127	C₂×C₄₁	1	1	yes	characteristic, complemented
291	C₂²×#124	C₂×C₄₁	1	1	yes	characteristic, complemented
292	C₂²×#121	C₂×C₄₁	1	1	yes	characteristic, complemented
293	#2431	C₂×C₄₁	1	16	yes	direct product factor
294	C₂×#392	C₂×C₄₁	1	4	yes	complemented
295	C₂×#391	C₂×C₄₁	1	1	yes	characteristic, complemented
296	C₂×#390	C₂×C₄₁	1	1	yes	characteristic, complemented
297	C₂×#386	C₂×C₄₁	1	4	yes	complemented
298	C₂×C₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
299	C₂×C₄₁	—	4	4	no	—
300	C₂×C₄₁	—	4	8	no	—
301	C₂×C₄₁	—	8	4	no	—
302	C₂×C₄₁	#2431	1	8	yes	direct product factor
303	C₂×C₄₁	C₂²×#120	1	1	yes	characteristic
304	C₂×C₄₁	C₂×#532	1	1	yes	characteristic
305	C₂×C₄₁	C₂×#535	1	1	yes	characteristic
306	C₂×C₄₁	C₂×#546	1	2	yes	—
307	C₂×C₄₁	C₂×#550	1	2	yes	—
308	C₂²×#41	—	2	8	no	—
309	C₂²×#41	—	2	8	no	—
310	C₂²×#41	—	2	8	no	—
311	C₂²×#41	C₂²×C₄₁	1	8	yes	complemented
312	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
313	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
314	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
315	C₂³×D₄	C₂²×C₄₁	1	4	yes	—
316	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
317	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
318	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
319	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
320	C₂×#127	—	2	8	no	—
321	C₂×#127	C₂²×C₄₁	1	8	yes	complemented
322	C₂×#124	—	2	8	no	—
323	C₂×#124	C₂²×C₄₁	1	8	yes	complemented
324	C₂×#121	—	2	8	no	—
325	C₂×#121	C₂²×C₄₁	1	8	yes	complemented
326	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
328	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
329	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
330	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
331	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
332	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
333	#392	C₂²×C₄₁	1	32	yes	complemented
334	#391	C₂²×C₄₁	1	8	yes	complemented
335	#390	C₂²×C₄₁	1	8	yes	complemented
336	#386	C₂²×C₄₁	1	32	yes	complemented
337	C₄×C₂²⋊C₄	C₂²×C₄₁	1	8	yes	complemented
338	C₂×#95	C₂²×C₄₁	1	4	yes	—
339	C₂×#95	C₂²×C₄₁	1	2	yes	—
340	C₄₁	C₂×#2431	1	1	yes	characteristic, direct product factor, Sylow
341	C₂⁵	C₂³×C₄₁	1	2	yes	—
342	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
343	C₂⁵	C₂³×C₄₁	1	2	yes	—
344	C₂×#41	—	2	128	no	—
345	C₂×#41	—	2	32	no	—
346	C₂×#41	—	2	32	no	—
347	C₂×#41	—	2	32	no	—
348	C₂²×Q₈	—	2	4	no	—
349	C₂²×Q₈	—	2	4	no	—
350	C₂²×Q₈	D₄×C₄₁	1	8	yes	complemented
351	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
352	C₂²×D₄	—	2	8	no	—
353	C₂²×D₄	—	2	8	no	—
354	C₂²×D₄	—	2	8	no	—
355	C₂²×D₄	—	2	16	no	—
356	C₂²×D₄	—	2	8	no	—
357	C₂²×D₄	—	2	4	no	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	—	2	4	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	—	2	4	no	—
362	C₂²×D₄	—	2	16	no	—
363	C₂²×D₄	—	4	8	no	—
364	C₂²×D₄	—	4	8	no	—
365	C₂²×D₄	D₄×C₄₁	1	8	yes	complemented
366	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
367	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
368	C₂²×D₄	C₂³×C₄₁	1	16	yes	—
369	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
370	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
371	C₂³×C₄	—	2	8	no	—
372	C₂³×C₄	—	2	8	no	—
373	C₂³×C₄	—	2	8	no	—
374	C₂³×C₄	—	2	4	no	—
375	C₂³×C₄	—	2	4	no	—
376	C₂³×C₄	D₄×C₄₁	1	8	yes	complemented
377	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
378	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
379	C₂³×C₄	C₂³×C₄₁	1	8	yes	—
380	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
382	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
383	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
384	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
385	#127	—	2	32	no	—
386	#124	—	2	32	no	—
387	#121	—	2	32	no	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
390	C₂×C₂²⋊C₄	—	2	8	no	—
391	C₂×C₂²⋊C₄	—	2	16	no	—
392	C₂×C₂²⋊C₄	—	2	8	no	—
393	C₂×C₂²⋊C₄	—	4	8	no	—
394	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	—
398	C₂×C₄²	—	2	4	no	—
399	C₂×C₄²	—	2	4	no	—
400	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
401	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
402	#95	C₂³×C₄₁	1	8	yes	—
403	#95	C₂³×C₄₁	1	16	yes	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	4	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	8	no	—
410	C₂⁴	—	2	8	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	2	8	no	—
416	C₂⁴	—	2	8	no	—
417	C₂⁴	C₂×D₄×C₄₁	1	8	yes	—
418	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
419	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
420	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
421	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
422	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
423	#41	—	2	256	no	—
424	C₂×Q₈	—	2	32	no	—
425	C₂×Q₈	—	2	8	no	—
426	C₂×Q₈	—	2	8	no	—
427	C₂×Q₈	C₂×D₄×C₄₁	1	16	yes	complemented
428	C₂×D₄	—	2	64	no	—
429	C₂×D₄	—	2	16	no	—
430	C₂×D₄	—	2	16	no	—
431	C₂×D₄	—	2	16	no	—
432	C₂×D₄	—	2	32	no	—
433	C₂×D₄	—	2	32	no	—
434	C₂×D₄	—	2	16	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	32	no	—
441	C₂×D₄	—	4	16	no	—
442	C₂×D₄	—	4	16	no	—
443	C₂×D₄	—	4	64	no	—
444	C₂×D₄	—	4	32	no	—
445	C₂×D₄	—	4	16	no	—
446	C₂×D₄	C₂×D₄×C₄₁	1	16	yes	complemented
447	C₂²×C₄	—	2	64	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	16	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	32	no	—
456	C₂²×C₄	—	2	16	no	—
457	C₂²×C₄	—	2	16	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	8	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
466	C₂²×C₄	C₂×D₄×C₄₁	1	8	yes	—
467	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
468	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
469	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
470	C₂²×C₄	C₂×D₄×C₄₁	1	16	yes	complemented
471	C₂²×C₄	#41×C₄₁	1	8	yes	complemented
472	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
478	C₄⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	16	no	—
480	C₂²⋊C₄	—	2	32	no	—
481	C₂²⋊C₄	—	2	16	no	—
482	C₂²⋊C₄	—	4	16	no	—
483	C₄²	—	2	8	no	—
484	C₄²	—	2	8	no	—
485	C₂³	—	2	16	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	32	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	8	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	4	8	no	—
504	C₂³	—	4	8	no	—
505	C₂³	—	4	8	no	—
506	C₂³	—	4	8	no	—
507	C₂³	—	4	16	no	—
508	C₂³	—	4	8	no	—
509	C₂³	—	4	8	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	16	no	—
512	C₂³	—	4	16	no	—
513	C₂³	C₂²×D₄×C₄₁	1	8	yes	—
514	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
515	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
516	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
517	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
518	C₂³	C₂×#41×C₄₁	1	4	yes	—
519	C₂³	H(5,𝔽₂)×C₄₁	1	4	yes	—
520	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
521	Q₈	—	2	32	no	—
522	D₄	—	2	64	no	—
523	D₄	—	2	32	no	—
524	D₄	—	4	64	no	—
525	D₄	—	4	32	no	—
526	D₄	—	4	16	no	—
527	C₂×C₄	—	2	64	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	16	no	—
530	C₂×C₄	—	2	16	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	32	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	4	8	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	#120×C₄₁	1	16	yes	—
546	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
547	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
548	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
549	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
550	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
551	C₂×C₄	C₂×#41×C₄₁	1	8	yes	complemented
552	C₂²	—	2	8	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	16	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	16	no	—
560	C₂²	—	4	32	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	8	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	8	no	—
568	C₂²	—	4	8	no	—
569	C₂²	—	8	16	no	—
570	C₂²	C₂×#120×C₄₁	1	4	yes	—
571	C₂²	C₄₁×#532	1	4	yes	—
572	C₂²	C₄₁×#535	1	4	yes	—
573	C₂²	C₄₁×#546	1	8	yes	—
574	C₂²	C₄₁×#550	1	8	yes	—
575	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
576	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
577	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
578	C₂²	C₂²×#41×C₄₁	1	2	yes	—
579	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
580	C₄	—	2	4	no	—
581	C₄	—	2	8	no	—
582	C₄	—	2	8	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	4	no	—
585	C₄	C₂×#120×C₄₁	1	8	yes	—
586	C₂	—	4	4	no	—
587	C₂	—	4	8	no	—
588	C₂	—	8	4	no	—
589	C₂	C₄₁×#2431	1	8	yes	direct product factor
590	C₂	C₂²×#120×C₄₁	1	1	yes	characteristic
591	C₂	C₂×C₄₁×#532	1	1	yes	characteristic
592	C₂	C₂×C₄₁×#535	1	1	yes	characteristic
593	C₂	C₂×C₄₁×#546	1	2	yes	—
594	C₂	C₂×C₄₁×#550	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
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
1. C₂³×#41×C₄₁	C₂	semidirect
2. C₂²×#127×C₄₁	C₂	semidirect
3. C₂²×#124×C₄₁	C₂	semidirect
4. C₂²×#121×C₄₁	C₂	semidirect
5. C₄₁×#2431	C₂	direct (N × H)
6. C₂×C₄₁×#392	C₂	semidirect
7. C₂×C₄₁×#391	C₂	semidirect
8. C₂×C₄₁×#390	C₂	semidirect
9. C₂×C₄₁×#386	C₂	semidirect
10. C₂×C₄×C₂²⋊C₄×C₄₁	C₂	semidirect
14. C₂²×#41×C₄₁	C₂²	semidirect
24. C₂×#127×C₄₁	C₂²	semidirect
26. C₂×#124×C₄₁	C₂²	semidirect
28. C₂×#121×C₄₁	C₂²	semidirect
36. C₄₁×#392	C₂²	semidirect
37. C₄₁×#391	C₂²	semidirect
38. C₄₁×#390	C₂²	semidirect
39. C₄₁×#386	C₂²	semidirect
40. C₄×C₂²⋊C₄×C₄₁	C₂²	semidirect
52. C₂²×Q₈×C₄₁	D₄	semidirect
67. C₂²×D₄×C₄₁	D₄	semidirect
78. C₂³×C₄×C₄₁	D₄	semidirect
129. C₂×Q₈×C₄₁	C₂×D₄	semidirect
148. C₂×D₄×C₄₁	C₂×D₄	semidirect
172. C₂²×C₄×C₄₁	C₂×D₄	semidirect
173. C₂²×C₄×C₄₁	#41	semidirect
253. C₂×C₄×C₄₁	C₂×#41	semidirect
254. C₂×#2431	C₄₁	direct (N × H)
289. C₂³×#41	C₂×C₄₁	semidirect
290. C₂²×#127	C₂×C₄₁	semidirect
291. C₂²×#124	C₂×C₄₁	semidirect
292. C₂²×#121	C₂×C₄₁	semidirect
293. #2431	C₂×C₄₁	direct (N × H)
294. C₂×#392	C₂×C₄₁	semidirect
295. C₂×#391	C₂×C₄₁	semidirect
296. C₂×#390	C₂×C₄₁	semidirect
297. C₂×#386	C₂×C₄₁	semidirect
298. C₂×C₄×C₂²⋊C₄	C₂×C₄₁	semidirect
302. C₂×C₄₁	#2431	direct (N × H)
311. C₂²×#41	C₂²×C₄₁	semidirect
321. C₂×#127	C₂²×C₄₁	semidirect
323. C₂×#124	C₂²×C₄₁	semidirect
325. C₂×#121	C₂²×C₄₁	semidirect
333. #392	C₂²×C₄₁	semidirect
334. #391	C₂²×C₄₁	semidirect
335. #390	C₂²×C₄₁	semidirect
336. #386	C₂²×C₄₁	semidirect
337. C₄×C₂²⋊C₄	C₂²×C₄₁	semidirect
340. C₄₁	C₂×#2431	direct (N × H)
350. C₂²×Q₈	D₄×C₄₁	semidirect
365. C₂²×D₄	D₄×C₄₁	semidirect
376. C₂³×C₄	D₄×C₄₁	semidirect
427. C₂×Q₈	C₂×D₄×C₄₁	semidirect
446. C₂×D₄	C₂×D₄×C₄₁	semidirect
470. C₂²×C₄	C₂×D₄×C₄₁	semidirect
471. C₂²×C₄	#41×C₄₁	semidirect
551. C₂×C₄	C₂×#41×C₄₁	semidirect
589. C₂	C₄₁×#2431	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₄₁	2
C₂²×#127×C₄₁	2
C₂²×#124×C₄₁	2
C₂²×#121×C₄₁	2
C₄₁×#2431	2
C₂×C₄₁×#392	2
C₂×C₄₁×#391	2
C₂×C₄₁×#390	2
C₂×C₄₁×#386	2
C₂×C₄×C₂²⋊C₄×C₄₁	2
C₂×#2431	41

Subgroups — C2×C41×#2431 #23810912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2431 #23810912