Subgroups — C₂×C₅×#4726 #14411624

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₅×#4726	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#407	—	3	1	no	maximal, Hall
8	C₂⁴×C₅×D₃	C₄	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₅×Dic₃	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	—	2	8	no	—
12	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
13	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₄	1	4	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
19	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
20	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
21	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	complemented
22	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
23	C₅×#830	C₂²	1	4	yes	complemented
24	C₅×(C₂×D₃)⋊C₈	C₂²	1	8	yes	complemented
25	C₂×#4726	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂⁴×C₄×C₅	—	3	1	no	—
27	C₂²×C₅×M₁₆	—	3	2	no	—
28	C₅×#407	—	3	8	no	—
29	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
30	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
31	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
32	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₅×D₃	—	2	4	no	—
34	C₂³×C₅×D₃	—	2	4	no	—
35	C₂³×C₅×D₃	—	2	4	no	—
36	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
37	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	4	no	—
45	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
47	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	—	2	4	no	—
49	C₂×C₄×C₅×D₃	—	2	4	no	—
50	C₂×C₄×C₅×D₃	—	2	4	no	—
51	C₂×C₄×C₅×D₃	—	2	16	no	—
52	C₂×C₄×C₅×D₃	—	2	16	no	—
53	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
54	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
56	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×C₅×D₃	D₄	1	8	yes	—
58	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
59	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
60	C₂×C₃×C₅×C₈	—	2	4	no	—
61	C₂×C₃×C₅×C₈	C₂³	1	4	yes	complemented
62	C₂×C₅×C₃⋊C₈	—	2	4	no	—
63	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	complemented
64	C₅×ΓL(1,𝔽₂₅)	—	2	16	no	—
65	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
66	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	2	yes	complemented
67	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	2	yes	complemented
70	#4726	C₂×C₅	1	8	yes	direct product factor
71	C₂⁵×C₅	—	3	1	no	—
72	C₂³×C₄×C₅	—	3	1	no	—
73	C₂³×C₄×C₅	—	3	1	no	—
74	C₂³×C₄×C₅	—	3	1	no	—
75	C₂³×C₄×C₅	—	3	4	no	—
76	C₂³×C₄×C₅	—	3	1	no	—
77	C₂³×C₄×C₅	—	3	4	no	—
78	C₂³×C₄×C₅	—	3	1	no	—
79	C₂³×C₄×C₅	—	6	8	no	—
80	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
81	C₂×C₅×M₁₆	—	3	8	no	—
82	C₂×C₅×M₁₆	—	6	8	no	—
83	C₂²×C₅×C₈	—	3	2	no	—
84	C₂²×C₅×C₈	C₂×D₃	1	2	yes	complemented
85	C₅×C₂²⋊C₈	—	3	4	no	—
86	C₅×C₂²⋊C₈	—	3	8	no	—
87	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	complemented
88	C₂×#407	—	3	1	no	Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	M₁₆	1	4	yes	complemented
92	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
93	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₅×D₃	—	2	32	no	—
95	C₂²×C₅×D₃	—	2	2	no	—
96	C₂²×C₅×D₃	—	2	2	no	—
97	C₂²×C₅×D₃	—	2	2	no	—
98	C₂²×C₅×D₃	—	2	2	no	—
99	C₂²×C₅×D₃	—	2	8	no	—
100	C₂²×C₅×D₃	—	2	8	no	—
101	C₂²×C₅×D₃	—	2	8	no	—
102	C₂²×C₅×D₃	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₅×D₃	M₁₆	1	4	yes	complemented
104	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	2	8	no	—
115	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
116	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
117	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
118	C₄×C₅×D₃	—	2	8	no	—
119	C₄×C₅×D₃	—	2	4	no	—
120	C₄×C₅×D₃	—	2	4	no	—
121	C₄×C₅×D₃	—	2	8	no	—
122	C₄×C₅×D₃	C₂²⋊C₄	1	8	yes	—
123	C₄×C₅×D₃	C₂×D₄	1	8	yes	—
124	C₃×C₅×C₈	—	2	4	no	—
125	C₅×C₃⋊C₈	—	2	4	no	—
126	C₂⁴×D₃	C₄×C₅	1	1	yes	characteristic
127	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂³×Dic₃	C₄×C₅	1	1	yes	characteristic
129	C₂²×C₄×D₃	—	2	8	no	—
130	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
131	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
132	C₂²×C₄×D₃	C₄×C₅	1	4	yes	—
133	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
134	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
135	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
137	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
138	C₂×ΓL(1,𝔽₂₅)	—	2	8	no	—
139	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	8	yes	complemented
140	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
141	#830	C₂²×C₅	1	4	yes	complemented
142	(C₂×D₃)⋊C₈	C₂²×C₅	1	8	yes	complemented
143	C₂⁴×C₅	—	3	1	no	—
144	C₂⁴×C₅	—	3	1	no	—
145	C₂⁴×C₅	—	3	4	no	—
146	C₂⁴×C₅	—	6	4	no	—
147	C₂⁴×C₅	—	6	4	no	—
148	C₂⁴×C₅	—	6	4	no	—
149	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
150	C₂²×C₄×C₅	—	2	4	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	3	2	no	—
153	C₂²×C₄×C₅	—	3	8	no	—
154	C₂²×C₄×C₅	—	3	2	no	—
155	C₂²×C₄×C₅	—	3	4	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	4	no	—
158	C₂²×C₄×C₅	—	3	4	no	—
159	C₂²×C₄×C₅	—	3	2	no	—
160	C₂²×C₄×C₅	—	3	2	no	—
161	C₂²×C₄×C₅	—	6	4	no	—
162	C₂²×C₄×C₅	—	6	16	no	—
163	C₂²×C₄×C₅	—	6	16	no	—
164	C₂²×C₄×C₅	—	6	4	no	—
165	C₂²×C₄×C₅	—	6	4	no	—
166	C₂²×C₄×C₅	—	6	4	no	—
167	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
169	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
171	C₅×M₁₆	—	6	16	no	—
172	C₂×C₅×C₈	—	2	4	no	—
173	C₂×C₅×C₈	—	3	4	no	—
174	C₂×C₅×C₈	—	6	4	no	—
175	C₂×C₅×C₈	C₂²×D₃	1	4	yes	complemented
176	C₂⁴×C₄	—	3	1	no	—
177	C₂²×M₁₆	—	3	2	no	—
178	#407	—	3	8	no	—
179	C₂×C₂²⋊C₈	—	3	1	no	—
180	C₂×C₂²⋊C₈	—	3	2	no	—
181	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
182	C₂²×C₃×C₅	—	2	2	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	—	2	8	no	—
185	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
187	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
188	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
189	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₅×D₃	—	2	32	no	—
191	C₂×C₅×D₃	—	2	2	no	—
192	C₂×C₅×D₃	—	2	2	no	—
193	C₂×C₅×D₃	—	2	2	no	—
194	C₂×C₅×D₃	—	2	2	no	—
195	C₂×C₅×D₃	—	2	8	no	—
196	C₂×C₅×D₃	—	2	8	no	—
197	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
198	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
199	C₃×C₄×C₅	—	2	2	no	—
200	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
201	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
202	C₅×Dic₃	—	2	2	no	—
203	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
204	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂³×D₃	—	2	4	no	—
206	C₂³×D₃	—	2	4	no	—
207	C₂³×D₃	—	2	4	no	—
208	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
209	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
211	C₂²×C₃×C₄	—	2	4	no	—
212	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
214	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
215	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	C₂²×Dic₃	—	2	4	no	—
217	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
219	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₄×D₃	—	2	4	no	—
221	C₂×C₄×D₃	—	2	4	no	—
222	C₂×C₄×D₃	—	2	4	no	—
223	C₂×C₄×D₃	—	2	16	no	—
224	C₂×C₄×D₃	—	2	16	no	—
225	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
226	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
227	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
228	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
229	C₂×C₄×D₃	C₅×D₄	1	8	yes	—
230	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
231	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
232	C₂×C₃×C₈	—	2	4	no	—
233	C₂×C₃×C₈	C₂³×C₅	1	4	yes	complemented
234	C₂×C₃⋊C₈	—	2	4	no	—
235	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	complemented
236	ΓL(1,𝔽₂₅)	—	2	16	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	3	4	no	—
240	C₂³×C₅	—	3	4	no	—
241	C₂³×C₅	—	3	2	no	—
242	C₂³×C₅	—	3	2	no	—
243	C₂³×C₅	—	6	8	no	—
244	C₂³×C₅	—	6	8	no	—
245	C₂³×C₅	—	6	32	no	—
246	C₂³×C₅	—	6	2	no	—
247	C₂³×C₅	—	6	2	no	—
248	C₂³×C₅	—	6	2	no	—
249	C₂³×C₅	—	6	8	no	—
250	C₂³×C₅	—	6	2	no	—
251	C₂³×C₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
252	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
253	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	4	no	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	—	3	4	no	—
258	C₂×C₄×C₅	—	3	2	no	—
259	C₂×C₄×C₅	—	3	8	no	—
260	C₂×C₄×C₅	—	3	8	no	—
261	C₂×C₄×C₅	—	3	2	no	—
262	C₂×C₄×C₅	—	6	8	no	—
263	C₂×C₄×C₅	—	6	8	no	—
264	C₂×C₄×C₅	—	6	8	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	4	no	—
267	C₂×C₄×C₅	—	6	4	no	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
269	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
270	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	C₅×C₈	—	2	4	no	—
273	C₅×C₈	—	6	4	no	—
274	C₂⁵	—	3	1	no	—
275	C₂³×C₄	—	3	1	no	—
276	C₂³×C₄	—	3	1	no	—
277	C₂³×C₄	—	3	1	no	—
278	C₂³×C₄	—	3	4	no	—
279	C₂³×C₄	—	3	1	no	—
280	C₂³×C₄	—	3	1	no	—
281	C₂³×C₄	—	3	4	no	—
282	C₂³×C₄	—	6	8	no	—
283	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
284	C₂×M₁₆	—	3	8	no	—
285	C₂×M₁₆	—	6	8	no	—
286	C₂²×C₈	—	3	2	no	—
287	C₂²×C₈	C₂×C₅×D₃	1	2	yes	complemented
288	C₂²⋊C₈	—	3	4	no	—
289	C₂²⋊C₈	—	3	8	no	—
290	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
291	C₂×C₃×C₅	—	2	4	no	—
292	C₂×C₃×C₅	#407	1	4	yes	complemented
293	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
295	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
296	C₅×D₃	—	2	4	no	—
297	C₅×D₃	—	2	4	no	—
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	C₅×M₁₆	1	4	yes	complemented
301	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
302	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂²×D₃	—	2	32	no	—
304	C₂²×D₃	—	2	2	no	—
305	C₂²×D₃	—	2	2	no	—
306	C₂²×D₃	—	2	2	no	—
307	C₂²×D₃	—	2	2	no	—
308	C₂²×D₃	—	2	8	no	—
309	C₂²×D₃	—	2	8	no	—
310	C₂²×D₃	—	2	8	no	—
311	C₂²×D₃	C₅×C₂²⋊C₄	1	4	yes	—
312	C₂²×D₃	C₅×M₁₆	1	4	yes	complemented
313	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
314	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
319	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
321	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
322	C₂×Dic₃	—	2	2	no	—
323	C₂×Dic₃	—	2	8	no	—
324	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
325	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
326	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
327	C₄×D₃	—	2	8	no	—
328	C₄×D₃	—	2	4	no	—
329	C₄×D₃	—	2	4	no	—
330	C₄×D₃	—	2	8	no	—
331	C₄×D₃	C₅×C₂²⋊C₄	1	8	yes	—
332	C₄×D₃	C₂×C₅×D₄	1	8	yes	—
333	C₃×C₈	—	2	4	no	—
334	C₃⋊C₈	—	2	4	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	2	8	no	—
338	C₂²×C₅	—	3	4	no	—
339	C₂²×C₅	—	3	4	no	—
340	C₂²×C₅	—	6	32	no	—
341	C₂²×C₅	—	6	2	no	—
342	C₂²×C₅	—	6	2	no	—
343	C₂²×C₅	—	6	2	no	—
344	C₂²×C₅	—	6	2	no	—
345	C₂²×C₅	—	6	8	no	—
346	C₂²×C₅	—	6	8	no	—
347	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
348	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
349	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
350	C₂²×C₅	D₃×M₁₆	1	2	yes	—
351	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	3	4	no	—
354	C₄×C₅	—	6	2	no	—
355	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
356	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
357	C₂⁴	—	3	1	no	—
358	C₂⁴	—	3	1	no	—
359	C₂⁴	—	3	4	no	—
360	C₂⁴	—	6	4	no	—
361	C₂⁴	—	6	4	no	—
362	C₂⁴	—	6	4	no	—
363	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	3	8	no	—
368	C₂²×C₄	—	3	2	no	—
369	C₂²×C₄	—	3	4	no	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	3	4	no	—
372	C₂²×C₄	—	3	4	no	—
373	C₂²×C₄	—	3	2	no	—
374	C₂²×C₄	—	3	2	no	—
375	C₂²×C₄	—	6	4	no	—
376	C₂²×C₄	—	6	16	no	—
377	C₂²×C₄	—	6	16	no	—
378	C₂²×C₄	—	6	4	no	—
379	C₂²×C₄	—	6	4	no	—
380	C₂²×C₄	—	6	4	no	—
381	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
382	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
383	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
384	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
385	M₁₆	—	6	16	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	3	4	no	—
388	C₂×C₈	—	6	4	no	—
389	C₂×C₈	C₂²×C₅×D₃	1	4	yes	complemented
390	C₃×C₅	C₂×#407	1	1	yes	characteristic, complemented, Hall
391	C₂²×C₃	—	2	8	no	—
392	C₂²×C₃	—	2	2	no	—
393	C₂²×C₃	—	2	2	no	—
394	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
395	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
396	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
397	C₂²×C₃	C₂×C₅×M₁₆	1	4	yes	complemented
398	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
399	C₂×D₃	—	2	32	no	—
400	C₂×D₃	—	2	8	no	—
401	C₂×D₃	—	2	8	no	—
402	C₂×D₃	—	2	2	no	—
403	C₂×D₃	—	2	2	no	—
404	C₂×D₃	—	2	2	no	—
405	C₂×D₃	—	2	2	no	—
406	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
407	C₂×D₃	C₂×C₅×M₁₆	1	4	yes	complemented
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
410	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
411	Dic₃	—	2	2	no	—
412	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
413	C₂×C₅	—	2	4	no	—
414	C₂×C₅	—	6	4	no	—
415	C₂×C₅	—	6	4	no	—
416	C₂×C₅	#4726	1	4	yes	direct product factor
417	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
418	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
419	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	3	4	no	—
423	C₂³	—	3	4	no	—
424	C₂³	—	3	2	no	—
425	C₂³	—	3	2	no	—
426	C₂³	—	6	8	no	—
427	C₂³	—	6	8	no	—
428	C₂³	—	6	32	no	—
429	C₂³	—	6	2	no	—
430	C₂³	—	6	2	no	—
431	C₂³	—	6	2	no	—
432	C₂³	—	6	8	no	—
433	C₂³	—	6	2	no	—
434	C₂³	C₅×ΓL(1,𝔽₂₅)	1	4	yes	complemented
435	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
436	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	3	4	no	—
441	C₂×C₄	—	3	2	no	—
442	C₂×C₄	—	3	8	no	—
443	C₂×C₄	—	3	8	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	6	8	no	—
446	C₂×C₄	—	6	8	no	—
447	C₂×C₄	—	6	8	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	4	no	—
450	C₂×C₄	—	6	4	no	—
451	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
452	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
453	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
454	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	6	4	no	—
457	C₂×C₃	—	2	4	no	—
458	C₂×C₃	C₅×#407	1	4	yes	complemented
459	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
461	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
462	D₃	—	2	4	no	—
463	D₃	—	2	4	no	—
464	C₅	C₂×#4726	1	1	yes	characteristic, direct product factor, Sylow
465	C₂²	—	2	8	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	3	4	no	—
469	C₂²	—	3	4	no	—
470	C₂²	—	6	32	no	—
471	C₂²	—	6	8	no	—
472	C₂²	—	6	8	no	—
473	C₂²	—	6	2	no	—
474	C₂²	—	6	2	no	—
475	C₂²	—	6	2	no	—
476	C₂²	—	6	2	no	—
477	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
478	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
479	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	4	yes	complemented
480	C₂²	C₅×D₃×M₁₆	1	2	yes	—
481	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	3	4	no	—
484	C₄	—	6	2	no	—
485	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
486	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
487	C₃	C₂×C₅×#407	1	1	yes	characteristic, complemented, Sylow
488	C₂	—	2	4	no	—
489	C₂	—	6	4	no	—
490	C₂	—	6	4	no	—
491	C₂	C₅×#4726	1	4	yes	direct product factor
492	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
493	C₂	C₂²×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
494	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₅×D₃	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₂×C₅×#407
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
4. C₂×C₅×#830	C₂	semidirect
5. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₅×#4726	C₂	direct (N × H)
18. C₂²×C₃×C₅×C₈	C₂²	semidirect
19. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
21. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
22. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
23. C₅×#830	C₂²	semidirect
24. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
25. C₂×#4726	C₅	direct (N × H)
31. C₂×C₅×C₂²⋊C₈	D₃	semidirect
61. C₂×C₃×C₅×C₈	C₂³	semidirect
63. C₂×C₅×C₃⋊C₈	C₂³	semidirect
66. C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
67. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
68. C₂×#830	C₂×C₅	semidirect
69. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
70. #4726	C₂×C₅	direct (N × H)
84. C₂²×C₅×C₈	C₂×D₃	semidirect
87. C₅×C₂²⋊C₈	C₂×D₃	semidirect
91. C₂³×C₃×C₅	M₁₆	semidirect
103. C₂²×C₅×D₃	M₁₆	semidirect
136. C₂²×C₃×C₈	C₂²×C₅	semidirect
137. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
139. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
140. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
141. #830	C₂²×C₅	semidirect
142. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
175. C₂×C₅×C₈	C₂²×D₃	semidirect
181. C₂×C₂²⋊C₈	C₅×D₃	semidirect
188. C₂²×C₃×C₅	C₂×M₁₆	semidirect
198. C₂×C₅×D₃	C₂×M₁₆	semidirect
233. C₂×C₃×C₈	C₂³×C₅	semidirect
235. C₂×C₃⋊C₈	C₂³×C₅	semidirect
251. C₂³×C₅	ΓL(1,𝔽₂₅)	semidirect
287. C₂²×C₈	C₂×C₅×D₃	semidirect
290. C₂²⋊C₈	C₂×C₅×D₃	semidirect
292. C₂×C₃×C₅	#407	semidirect
300. C₂³×C₃	C₅×M₁₆	semidirect
312. C₂²×D₃	C₅×M₁₆	semidirect
349. C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
389. C₂×C₈	C₂²×C₅×D₃	semidirect
390. C₃×C₅	C₂×#407	semidirect
397. C₂²×C₃	C₂×C₅×M₁₆	semidirect
407. C₂×D₃	C₂×C₅×M₁₆	semidirect
416. C₂×C₅	#4726	direct (N × H)
434. C₂³	C₅×ΓL(1,𝔽₂₅)	semidirect
458. C₂×C₃	C₅×#407	semidirect
464. C₅	C₂×#4726	direct (N × H)
479. C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	semidirect
487. C₃	C₂×C₅×#407	semidirect
491. C₂	C₅×#4726	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×C₄×C₅×D₃	2
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#830	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₅×#4726	2
C₂×C₅×#407	3
C₂×#4726	5

Subgroups — C2×C5×#4726 #14411624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4726 #14411624