Subgroups — D₅⋊#5011 #14414708

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊#208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₅⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	#11752432	C₂	1	2	yes	maximal, complemented
5	D₅⋊#830	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅⋊#830	C₂	1	1	yes	maximal, characteristic, complemented
7	#11752363	C₂	1	2	yes	maximal, complemented
8	#11752353	C₂	1	2	yes	maximal, complemented
9	#11752352	C₂	1	2	yes	maximal, complemented
10	D₅⋊(C₄⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
11	#11752335	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅⋊#435	—	3	1	no	maximal, Hall
13	C₂×C₃×D₄×D₅	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×#6762	C₂²	1	2	yes	complemented
17	C₂²×C₃⋊#170	C₂²	1	2	yes	complemented
18	D₅⋊#208	—	2	4	no	—
19	C₂×#6758	C₂²	1	2	yes	complemented
20	C₂×D₅⋊(C₃⋊C₈)	—	2	4	no	—
21	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
26	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
27	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
29	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
30	C₃×#4039	C₂²	1	1	yes	characteristic
31	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
32	C₃×#4027	C₂²	1	1	yes	characteristic
33	C₃×#4027	C₂²	1	1	yes	characteristic
34	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
35	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
36	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
37	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
38	#91241	C₂²	1	2	yes	complemented
39	#91241	C₂²	1	2	yes	complemented
40	#91233	C₂²	1	2	yes	complemented
41	#91232	C₂²	1	2	yes	complemented
42	#91232	C₂²	1	2	yes	complemented
43	#91231	C₂²	1	2	yes	complemented
44	#91231	C₂²	1	2	yes	complemented
45	C₄⋊(C₃⋊#170)	C₂²	1	2	yes	complemented
46	C₂×#5011	—	5	1	no	maximal, Hall
47	C₂×D₅⋊M₁₆	—	3	1	no	—
48	C₂²×D₅⋊C₈	—	3	1	no	—
49	C₄×D₄×D₅	D₃	1	1	yes	characteristic
50	#65773	—	3	2	no	—
51	D₅⋊(C₂²⋊C₈)	—	3	1	no	—
52	D₅⋊(C₂²⋊C₈)	—	3	1	no	—
53	#65704	—	3	2	no	—
54	#65694	—	3	2	no	—
55	#65693	—	3	2	no	—
56	D₅⋊(C₄⋊C₈)	—	3	1	no	—
57	#65676	—	3	1	no	—
58	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
67	C₃×D₄×D₅	—	2	4	no	—
68	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	—	2	2	no	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₂×C₃×C₄×D₅	—	2	2	no	—
72	C₂×C₃×C₄×D₅	—	2	2	no	—
73	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
82	#6762	—	2	4	no	—
83	C₂×C₃⋊#170	—	2	4	no	—
84	C₂×C₃⋊#170	C₂³	1	2	yes	—
85	C₂×C₃⋊#170	C₂³	1	2	yes	—
86	C₂×C₃⋊#170	C₂³	1	2	yes	—
87	C₂×C₃⋊#170	C₂³	1	2	yes	—
88	#6758	—	2	4	no	—
89	D₅⋊(C₃⋊C₈)	—	2	2	no	—
90	D₅⋊(C₃⋊C₈)	—	2	2	no	—
91	D₅⋊(C₃⋊C₈)	—	2	2	no	—
92	D₅⋊(C₃⋊C₈)	—	2	4	no	—
93	D₅⋊(C₃⋊C₈)	D₄	1	4	yes	complemented
94	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
98	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
100	C₃×#685	C₂×C₄	1	1	yes	characteristic
101	C₃×#685	C₂×C₄	1	1	yes	characteristic
102	C₃×#685	C₂×C₄	1	1	yes	characteristic
103	C₃×#685	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
105	C₃×#683	C₂×C₄	1	1	yes	characteristic
106	C₃×#683	C₂×C₄	1	1	yes	characteristic
107	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
108	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
109	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₄×D₄	—	5	1	no	—
111	C₂²×#208	—	5	1	no	—
112	C₂³×C₃⋊C₈	—	5	1	no	—
113	C₂×#830	—	5	1	no	—
114	C₂×#830	—	5	1	no	—
115	#5011	—	5	2	no	—
116	#5011	—	5	2	no	—
117	#5011	—	5	2	no	—
118	#5011	—	5	2	no	—
119	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
120	C₂×#803	—	5	1	no	—
121	C₂×D₄×D₅	Dic₃	1	1	yes	characteristic
122	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
123	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
124	C₂×#704	—	3	2	no	—
125	C₂²×#170	—	3	2	no	—
126	D₅⋊M₁₆	—	6	4	no	—
127	C₂×#700	—	3	2	no	—
128	C₂×D₅⋊C₈	—	3	1	no	—
129	C₂×D₅⋊C₈	—	3	1	no	—
130	C₂×D₅⋊C₈	—	3	1	no	—
131	C₂×D₅⋊C₈	—	3	1	no	—
132	C₂×D₅⋊C₈	—	3	2	no	—
133	C₂×D₅⋊C₈	—	6	4	no	—
134	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
135	D₄×Dic₅	C₂×D₃	1	1	yes	characteristic
136	C₄×C₂²⋊D₅	Dic₃	1	1	yes	characteristic
137	C₄×C₂²⋊D₅	Dic₃	1	1	yes	characteristic
138	#4039	C₂×D₃	1	1	yes	characteristic
139	D₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
140	#4027	C₂×D₃	1	1	yes	characteristic
141	#4027	C₂×D₃	1	1	yes	characteristic
142	D₅×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
143	D₅×C₂²⋊C₄	Dic₃	1	1	yes	characteristic
144	C₄×D₂₀	Dic₃	1	1	yes	characteristic
145	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
146	C₂²⋊#170	—	3	2	no	—
147	C₂²⋊#170	—	3	2	no	—
148	#4004	—	3	2	no	—
149	#4003	—	3	2	no	—
150	#4003	—	3	2	no	—
151	#4002	—	3	2	no	—
152	#4002	—	3	2	no	—
153	C₄⋊#170	—	3	2	no	—
154	C₂×#435	—	15	1	no	Sylow
155	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₃×D₅	—	2	2	no	—
158	C₂²×C₃×D₅	—	2	2	no	—
159	C₂²×C₃×D₅	—	2	2	no	—
160	C₂²×C₃×D₅	—	2	2	no	—
161	C₂²×C₃×D₅	—	2	2	no	—
162	C₂²×C₃×D₅	M₁₆	1	4	yes	complemented
163	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
166	C₃×C₅×D₄	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₃×C₂²⋊D₅	—	2	2	no	—
175	C₃×C₂²⋊D₅	—	2	2	no	—
176	C₂×C₃×Dic₅	—	2	1	no	—
177	C₂×C₃×Dic₅	—	2	1	no	—
178	C₂×C₃×Dic₅	—	2	1	no	—
179	C₂×C₃×Dic₅	—	2	1	no	—
180	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
185	C₃×D₂₀	—	2	2	no	—
186	C₃×C₄×D₅	—	2	2	no	—
187	C₃×C₄×D₅	—	2	2	no	—
188	C₃×C₄×D₅	—	2	2	no	—
189	C₃×C₄×D₅	—	2	2	no	—
190	C₃×C₄×D₅	—	2	2	no	—
191	C₃×C₄×D₅	—	2	2	no	—
192	C₃×C₄×D₅	—	2	1	no	—
193	C₃×C₄×D₅	—	2	1	no	—
194	C₃×C₄×D₅	—	2	1	no	—
195	C₃×C₄×D₅	—	2	1	no	—
196	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
197	C₃×C₄×D₅	#41	1	2	yes	—
198	C₃⋊#170	—	2	2	no	—
199	C₃⋊#170	—	2	2	no	—
200	C₃⋊#170	—	2	2	no	—
201	C₃⋊#170	C₂×D₄	1	4	yes	complemented
202	C₂²×C₃×D₄	—	5	1	no	—
203	C₂³×C₃×C₄	—	5	1	no	—
204	C₂³×C₃×C₄	—	5	1	no	—
205	C₃×C₄×D₄	—	5	1	no	—
206	C₃×C₄×D₄	—	5	1	no	—
207	C₃×C₄×D₄	—	5	1	no	—
208	C₃×C₄×D₄	—	5	1	no	—
209	C₃×C₄×D₄	—	5	1	no	—
210	C₃×C₄×D₄	—	5	1	no	—
211	C₃×C₄×D₄	—	5	1	no	—
212	C₃×C₄×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	—	5	1	no	—
214	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
215	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
216	C₂×C₃×C₄²	—	5	1	no	—
217	C₂×#208	—	5	2	no	—
218	C₂×#208	—	5	2	no	—
219	C₂×#208	—	10	4	no	—
220	C₂²×C₃⋊C₈	—	5	1	no	—
221	C₂²×C₃⋊C₈	—	5	1	no	—
222	C₂²×C₃⋊C₈	—	5	1	no	—
223	C₂²×C₃⋊C₈	—	5	1	no	—
224	C₂²×C₃⋊C₈	—	5	2	no	—
225	C₂²×C₃⋊C₈	—	5	2	no	—
226	C₂²×C₃⋊C₈	—	10	4	no	—
227	#830	—	5	2	no	—
228	#830	—	5	2	no	—
229	#830	—	5	2	no	—
230	#830	—	5	2	no	—
231	C₄⋊(C₃⋊C₈)	—	5	2	no	—
232	C₄⋊(C₃⋊C₈)	—	5	2	no	—
233	#803	—	5	2	no	—
234	#803	—	5	2	no	—
235	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
236	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
237	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
240	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
241	C₂×C₂²⋊D₅	C₂×Dic₃	1	1	yes	characteristic
242	C₂²×Dic₅	C₂²×D₃	1	1	yes	characteristic
243	C₂²×Dic₅	C₂²×D₃	1	1	yes	characteristic
244	D₄×D₅	—	2	4	no	—
245	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
246	C₂×C₄×D₅	—	2	2	no	—
247	C₂×C₄×D₅	—	2	2	no	—
248	C₂×C₄×D₅	—	2	2	no	—
249	C₂×C₄×D₅	—	2	2	no	—
250	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
251	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
252	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
253	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
254	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
255	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
256	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
257	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
258	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
259	#704	—	6	4	no	—
260	C₂×#170	—	3	2	no	—
261	C₂×#170	—	3	2	no	—
262	C₂×#170	—	3	2	no	—
263	C₂×#170	—	3	2	no	—
264	C₂×#170	—	6	4	no	—
265	#700	—	6	4	no	—
266	D₅⋊C₈	—	3	4	no	—
267	D₅⋊C₈	—	6	4	no	—
268	D₅⋊C₈	—	6	2	no	—
269	D₅⋊C₈	—	6	2	no	—
270	D₅⋊C₈	—	6	2	no	—
271	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
272	C₅×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
273	C₅×C₂²⋊C₄	C₂×Dic₃	1	1	yes	characteristic
274	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
275	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
276	C₂²⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
277	#685	C₂×Dic₃	1	1	yes	characteristic
278	#685	C₂×Dic₃	1	1	yes	characteristic
279	#685	C₂×Dic₃	1	1	yes	characteristic
280	#685	C₂×Dic₃	1	1	yes	characteristic
281	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
282	#683	C₂×Dic₃	1	1	yes	characteristic
283	#683	C₂×Dic₃	1	1	yes	characteristic
284	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
285	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
286	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
287	C₂²×M₁₆	—	15	1	no	—
288	C₂³×C₈	—	15	1	no	—
289	C₂×C₄×D₄	—	5	1	no	—
290	#435	—	15	2	no	—
291	#435	—	15	2	no	—
292	#435	—	15	2	no	—
293	#435	—	15	2	no	—
294	C₂×C₄⋊C₈	—	15	1	no	—
295	C₂×C₂²⋊C₈	—	15	1	no	—
296	C₂×C₂²⋊C₈	—	15	1	no	—
297	C₂×#97	—	15	1	no	—
298	C₂²×C₃×C₅	—	2	1	no	—
299	C₂²×C₃×C₅	—	2	1	no	—
300	C₂²×C₃×C₅	—	2	1	no	—
301	C₂²×C₃×C₅	—	2	1	no	—
302	C₂²×C₃×C₅	—	2	1	no	—
303	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
304	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₃×D₅	—	2	1	no	—
306	C₂×C₃×D₅	—	2	1	no	—
307	C₂×C₃×D₅	—	2	8	no	—
308	C₂×C₃×D₅	—	2	1	no	—
309	C₂×C₃×D₅	—	2	1	no	—
310	C₂×C₃×D₅	—	2	1	no	—
311	C₂×C₃×D₅	—	4	4	no	—
312	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
313	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
314	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	complemented
315	C₂×C₃×D₅	#131	1	2	yes	—
316	C₃×C₄×C₅	—	2	1	no	—
317	C₃×C₄×C₅	—	2	1	no	—
318	C₃×C₄×C₅	—	2	1	no	—
319	C₃×C₄×C₅	—	2	1	no	—
320	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
321	C₃×Dic₅	—	2	1	no	—
322	C₃×Dic₅	—	2	1	no	—
323	C₃×Dic₅	—	2	1	no	—
324	C₃×Dic₅	—	2	1	no	—
325	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
326	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
327	C₂⁴×C₃	—	5	1	no	—
328	C₂⁴×C₃	—	5	1	no	—
329	C₂×C₃×D₄	—	5	1	no	—
330	C₂×C₃×D₄	—	5	1	no	—
331	C₂×C₃×D₄	—	5	1	no	—
332	C₂×C₃×D₄	—	10	4	no	—
333	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
334	C₂²×C₃×C₄	—	5	1	no	—
335	C₂²×C₃×C₄	—	5	1	no	—
336	C₂²×C₃×C₄	—	5	1	no	—
337	C₂²×C₃×C₄	—	5	1	no	—
338	C₂²×C₃×C₄	—	5	1	no	—
339	C₂²×C₃×C₄	—	5	1	no	—
340	C₂²×C₃×C₄	—	5	1	no	—
341	C₂²×C₃×C₄	—	5	1	no	—
342	C₂²×C₃×C₄	—	5	1	no	—
343	C₂²×C₃×C₄	—	5	1	no	—
344	C₂²×C₃×C₄	—	5	1	no	—
345	C₂²×C₃×C₄	—	10	2	no	—
346	C₂²×C₃×C₄	—	10	2	no	—
347	C₂²×C₃×C₄	—	10	2	no	—
348	C₂²×C₃×C₄	—	10	2	no	—
349	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₃×C₄⋊C₄	—	5	1	no	—
352	C₃×C₄⋊C₄	—	5	1	no	—
353	C₃×C₄⋊C₄	—	5	1	no	—
354	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₃×C₂²⋊C₄	—	5	1	no	—
356	C₃×C₂²⋊C₄	—	5	1	no	—
357	C₃×C₂²⋊C₄	—	5	1	no	—
358	C₃×C₂²⋊C₄	—	5	1	no	—
359	C₃×C₂²⋊C₄	—	5	1	no	—
360	C₃×C₂²⋊C₄	—	5	1	no	—
361	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
362	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
363	C₃×C₄²	—	5	1	no	—
364	C₃×C₄²	—	5	1	no	—
365	C₃×C₄²	—	5	1	no	—
366	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
367	#208	—	10	4	no	—
368	#208	—	10	4	no	—
369	C₂×C₃⋊C₈	—	5	2	no	—
370	C₂×C₃⋊C₈	—	5	4	no	—
371	C₂×C₃⋊C₈	—	5	2	no	—
372	C₂×C₃⋊C₈	—	5	2	no	—
373	C₂×C₃⋊C₈	—	5	2	no	—
374	C₂×C₃⋊C₈	—	10	4	no	—
375	C₂×C₃⋊C₈	—	10	4	no	—
376	C₂×C₃⋊C₈	—	10	2	no	—
377	C₂×C₃⋊C₈	—	10	2	no	—
378	C₂×C₃⋊C₈	—	10	2	no	—
379	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
380	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
381	C₂²×D₅	—	2	2	no	—
382	C₂²×D₅	—	2	2	no	—
383	C₂²×D₅	—	2	2	no	—
384	C₂²×D₅	—	2	2	no	—
385	C₂²×D₅	—	2	2	no	—
386	C₂²×D₅	#208	1	4	yes	complemented
387	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
388	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
389	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
390	C₅×D₄	—	2	2	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
394	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
395	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
396	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
397	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
398	C₂²⋊D₅	—	2	2	no	—
399	C₂²⋊D₅	—	2	2	no	—
400	C₂×Dic₅	—	2	1	no	—
401	C₂×Dic₅	—	2	1	no	—
402	C₂×Dic₅	—	2	1	no	—
403	C₂×Dic₅	—	2	1	no	—
404	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
405	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
406	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
407	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
408	C₂×Dic₅	C₂³×D₃	1	1	yes	characteristic
409	D₂₀	—	2	2	no	—
410	C₄×D₅	—	2	2	no	—
411	C₄×D₅	—	2	2	no	—
412	C₄×D₅	—	2	2	no	—
413	C₄×D₅	—	2	2	no	—
414	C₄×D₅	—	2	2	no	—
415	C₄×D₅	—	2	2	no	—
416	C₄×D₅	—	2	1	no	—
417	C₄×D₅	—	2	1	no	—
418	C₄×D₅	—	2	1	no	—
419	C₄×D₅	—	2	1	no	—
420	C₄×D₅	D₃×D₄	1	2	yes	—
421	C₄×D₅	#237	1	2	yes	—
422	#170	—	3	4	no	—
423	#170	—	6	2	no	—
424	#170	—	6	2	no	—
425	#170	—	6	2	no	—
426	C₂²×D₄	—	5	1	no	—
427	C₂³×C₄	—	5	1	no	—
428	C₂³×C₄	—	5	1	no	—
429	C₂×M₁₆	—	15	2	no	—
430	C₂×M₁₆	—	15	2	no	—
431	C₂×M₁₆	—	30	4	no	—
432	C₂²×C₈	—	15	1	no	—
433	C₂²×C₈	—	15	1	no	—
434	C₂²×C₈	—	15	2	no	—
435	C₂²×C₈	—	15	1	no	—
436	C₂²×C₈	—	15	1	no	—
437	C₂²×C₈	—	15	2	no	—
438	C₂²×C₈	—	30	4	no	—
439	C₄×D₄	—	5	1	no	—
440	C₄×D₄	—	5	1	no	—
441	C₄×D₄	—	5	1	no	—
442	C₄×D₄	—	5	1	no	—
443	C₄×D₄	—	5	1	no	—
444	C₄×D₄	—	5	1	no	—
445	C₄×D₄	—	5	1	no	—
446	C₄×D₄	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	5	1	no	—
448	C₂×C₂²⋊C₄	—	5	1	no	—
449	C₂×C₂²⋊C₄	—	5	1	no	—
450	C₂×C₄²	—	5	1	no	—
451	C₄⋊C₈	—	15	2	no	—
452	C₄⋊C₈	—	15	2	no	—
453	C₂²⋊C₈	—	15	2	no	—
454	C₂²⋊C₈	—	15	2	no	—
455	C₂²⋊C₈	—	15	2	no	—
456	C₂²⋊C₈	—	15	2	no	—
457	#97	—	15	2	no	—
458	#97	—	15	2	no	—
459	C₂×C₃×C₅	—	2	2	no	—
460	C₂×C₃×C₅	—	4	1	no	—
461	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
462	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
463	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
464	C₃×D₅	—	2	2	no	—
465	C₃×D₅	—	4	1	no	—
466	C₃×D₅	#435	1	4	yes	complemented
467	C₂³×C₃	—	5	1	no	—
468	C₂³×C₃	—	5	4	no	—
469	C₂³×C₃	—	5	1	no	—
470	C₂³×C₃	—	5	1	no	—
471	C₂³×C₃	—	10	2	no	—
472	C₂³×C₃	—	10	2	no	—
473	C₂³×C₃	—	10	2	no	—
474	C₂³×C₃	—	10	2	no	—
475	C₂³×C₃	—	10	2	no	—
476	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₃×D₄	—	2	2	no	—
479	C₃×D₄	—	10	2	no	—
480	C₃×D₄	—	10	2	no	—
481	C₃×D₄	—	10	2	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	5	1	no	—
485	C₂×C₃×C₄	—	5	2	no	—
486	C₂×C₃×C₄	—	5	2	no	—
487	C₂×C₃×C₄	—	5	1	no	—
488	C₂×C₃×C₄	—	5	1	no	—
489	C₂×C₃×C₄	—	5	1	no	—
490	C₂×C₃×C₄	—	5	1	no	—
491	C₂×C₃×C₄	—	10	1	no	—
492	C₂×C₃×C₄	—	10	1	no	—
493	C₂×C₃×C₄	—	10	1	no	—
494	C₂×C₃×C₄	—	10	1	no	—
495	C₂×C₃×C₄	—	10	2	no	—
496	C₂×C₃×C₄	—	10	2	no	—
497	C₂×C₃×C₄	—	10	2	no	—
498	C₂×C₃×C₄	—	10	2	no	—
499	C₂×C₃×C₄	—	10	1	no	—
500	C₂×C₃×C₄	—	10	1	no	—
501	C₂×C₃×C₄	—	10	1	no	—
502	C₂×C₃×C₄	—	10	1	no	—
503	C₂×C₃×C₄	—	10	2	no	—
504	C₂×C₃×C₄	—	10	2	no	—
505	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
509	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
510	C₃⋊C₈	—	5	4	no	—
511	C₃⋊C₈	—	10	2	no	—
512	C₃⋊C₈	—	10	2	no	—
513	C₃⋊C₈	—	10	2	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	1	no	—
516	C₂²×C₅	—	2	1	no	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	C₂×#208	1	2	yes	complemented
520	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
521	C₂×D₅	—	2	1	no	—
522	C₂×D₅	—	2	1	no	—
523	C₂×D₅	—	2	8	no	—
524	C₂×D₅	—	2	1	no	—
525	C₂×D₅	—	2	1	no	—
526	C₂×D₅	—	2	1	no	—
527	C₂×D₅	—	4	4	no	—
528	C₂×D₅	C₂×#208	1	2	yes	—
529	C₂×D₅	C₂×#208	1	2	yes	complemented
530	C₂×D₅	D₄×Dic₃	1	2	yes	—
531	C₂×D₅	#948	1	2	yes	—
532	C₄×C₅	—	2	1	no	—
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	—	2	1	no	—
535	C₄×C₅	—	2	1	no	—
536	C₄×C₅	D₄×Dic₃	1	2	yes	—
537	Dic₅	—	2	1	no	—
538	Dic₅	—	2	1	no	—
539	Dic₅	—	2	1	no	—
540	Dic₅	—	2	1	no	—
541	Dic₅	C₂×D₃×D₄	1	1	yes	characteristic
542	Dic₅	C₂×#237	1	1	yes	characteristic
543	C₂⁴	—	5	1	no	—
544	C₂⁴	—	5	1	no	—
545	C₂×D₄	—	5	1	no	—
546	C₂×D₄	—	5	1	no	—
547	C₂×D₄	—	5	1	no	—
548	C₂×D₄	—	10	4	no	—
549	C₂×D₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
550	C₂²×C₄	—	5	1	no	—
551	C₂²×C₄	—	5	1	no	—
552	C₂²×C₄	—	5	1	no	—
553	C₂²×C₄	—	5	1	no	—
554	C₂²×C₄	—	5	1	no	—
555	C₂²×C₄	—	5	1	no	—
556	C₂²×C₄	—	5	1	no	—
557	C₂²×C₄	—	5	1	no	—
558	C₂²×C₄	—	5	1	no	—
559	C₂²×C₄	—	5	1	no	—
560	C₂²×C₄	—	5	1	no	—
561	C₂²×C₄	—	10	2	no	—
562	C₂²×C₄	—	10	2	no	—
563	C₂²×C₄	—	10	2	no	—
564	C₂²×C₄	—	10	2	no	—
565	C₂²×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
566	C₂²×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
567	M₁₆	—	30	4	no	—
568	M₁₆	—	30	4	no	—
569	C₂×C₈	—	15	2	no	—
570	C₂×C₈	—	15	4	no	—
571	C₂×C₈	—	15	2	no	—
572	C₂×C₈	—	15	2	no	—
573	C₂×C₈	—	15	2	no	—
574	C₂×C₈	—	30	4	no	—
575	C₂×C₈	—	30	4	no	—
576	C₂×C₈	—	30	2	no	—
577	C₂×C₈	—	30	2	no	—
578	C₂×C₈	—	30	2	no	—
579	C₄⋊C₄	—	5	1	no	—
580	C₄⋊C₄	—	5	1	no	—
581	C₄⋊C₄	—	5	1	no	—
582	C₄⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
583	C₂²⋊C₄	—	5	1	no	—
584	C₂²⋊C₄	—	5	1	no	—
585	C₂²⋊C₄	—	5	1	no	—
586	C₂²⋊C₄	—	5	1	no	—
587	C₂²⋊C₄	—	5	1	no	—
588	C₂²⋊C₄	—	5	1	no	—
589	C₂²⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
590	C₂²⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
591	C₄²	—	5	1	no	—
592	C₄²	—	5	1	no	—
593	C₄²	—	5	1	no	—
594	C₄²	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
595	C₃×C₅	C₂×#435	1	1	yes	characteristic, complemented, Hall
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	5	2	no	—
602	C₂²×C₃	—	5	2	no	—
603	C₂²×C₃	—	5	2	no	—
604	C₂²×C₃	—	5	2	no	—
605	C₂²×C₃	—	10	8	no	—
606	C₂²×C₃	—	10	1	no	—
607	C₂²×C₃	—	10	1	no	—
608	C₂²×C₃	—	10	1	no	—
609	C₂²×C₃	—	10	1	no	—
610	C₂²×C₃	—	10	1	no	—
611	C₂²×C₃	—	20	4	no	—
612	C₂²×C₃	D₅⋊M₁₆	1	2	yes	complemented
613	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
614	C₃×C₄	—	2	1	no	—
615	C₃×C₄	—	2	1	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	5	1	no	—
619	C₃×C₄	—	5	1	no	—
620	C₃×C₄	—	10	1	no	—
621	C₃×C₄	—	10	1	no	—
622	C₃×C₄	—	10	1	no	—
623	C₃×C₄	—	10	1	no	—
624	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
625	C₂×C₅	—	2	2	no	—
626	C₂×C₅	—	4	1	no	—
627	C₂×C₅	C₂²×#208	1	1	yes	characteristic
628	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
629	C₂×C₅	C₂×#948	1	1	yes	characteristic
630	D₅	—	2	2	no	—
631	D₅	—	4	1	no	—
632	D₅	#5011	1	4	yes	complemented
633	C₂³	—	5	1	no	—
634	C₂³	—	5	4	no	—
635	C₂³	—	5	1	no	—
636	C₂³	—	5	1	no	—
637	C₂³	—	10	2	no	—
638	C₂³	—	10	2	no	—
639	C₂³	—	10	2	no	—
640	C₂³	—	10	2	no	—
641	C₂³	—	10	2	no	—
642	C₂³	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
643	C₂³	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
644	D₄	—	2	2	no	—
645	D₄	—	10	2	no	—
646	D₄	—	10	2	no	—
647	D₄	—	10	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	5	1	no	—
651	C₂×C₄	—	5	2	no	—
652	C₂×C₄	—	5	2	no	—
653	C₂×C₄	—	5	1	no	—
654	C₂×C₄	—	5	1	no	—
655	C₂×C₄	—	5	1	no	—
656	C₂×C₄	—	5	1	no	—
657	C₂×C₄	—	10	1	no	—
658	C₂×C₄	—	10	1	no	—
659	C₂×C₄	—	10	1	no	—
660	C₂×C₄	—	10	1	no	—
661	C₂×C₄	—	10	2	no	—
662	C₂×C₄	—	10	2	no	—
663	C₂×C₄	—	10	2	no	—
664	C₂×C₄	—	10	2	no	—
665	C₂×C₄	—	10	1	no	—
666	C₂×C₄	—	10	1	no	—
667	C₂×C₄	—	10	1	no	—
668	C₂×C₄	—	10	1	no	—
669	C₂×C₄	—	10	2	no	—
670	C₂×C₄	—	10	2	no	—
671	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
672	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
673	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
674	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
675	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
676	C₈	—	15	4	no	—
677	C₈	—	30	2	no	—
678	C₈	—	30	2	no	—
679	C₈	—	30	2	no	—
680	C₂×C₃	—	2	2	no	—
681	C₂×C₃	—	4	1	no	—
682	C₂×C₃	—	5	4	no	—
683	C₂×C₃	—	10	2	no	—
684	C₂×C₃	—	20	1	no	—
685	C₂×C₃	C₂×D₅⋊M₁₆	1	1	yes	characteristic
686	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
687	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
688	C₅	C₂×#5011	1	1	yes	characteristic, complemented, Sylow
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	5	2	no	—
695	C₂²	—	5	2	no	—
696	C₂²	—	5	2	no	—
697	C₂²	—	5	2	no	—
698	C₂²	—	10	8	no	—
699	C₂²	—	10	1	no	—
700	C₂²	—	10	1	no	—
701	C₂²	—	10	1	no	—
702	C₂²	—	10	1	no	—
703	C₂²	—	10	1	no	—
704	C₂²	—	20	4	no	—
705	C₂²	D₅⋊#208	1	2	yes	complemented
706	C₂²	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	5	1	no	—
712	C₄	—	5	1	no	—
713	C₄	—	10	1	no	—
714	C₄	—	10	1	no	—
715	C₄	—	10	1	no	—
716	C₄	—	10	1	no	—
717	C₄	D₄×ΓL(1,𝔽₁₆)	1	2	yes	—
718	C₃	D₅⋊#435	1	1	yes	characteristic, complemented, Sylow
719	C₂	—	2	2	no	—
720	C₂	—	4	1	no	—
721	C₂	—	5	4	no	—
722	C₂	—	10	2	no	—
723	C₂	—	20	1	no	—
724	C₂	C₂×D₅⋊#208	1	1	yes	characteristic
725	C₂	C₂×D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
726	C₂	D₅⋊#948	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂²	C₂³×ΓL(1,𝔽₁₆)
Fitting	C₃×C₄×C₅×D₄	C₄
prime radical	C₂×C₃×D₄×D₅	C₄
cosocle	C₂×C₃×Dic₅	C₂⁴
hypercenter	C₄×D₄	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₂×#435
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₅⋊#208	C₂	semidirect
2. C₂²×D₅⋊(C₃⋊C₈)	C₂	semidirect
4. #11752432	C₂	semidirect
5. D₅⋊#830	C₂	semidirect
6. D₅⋊#830	C₂	semidirect
7. #11752363	C₂	semidirect
8. #11752353	C₂	semidirect
9. #11752352	C₂	semidirect
10. D₅⋊(C₄⋊(C₃⋊C₈))	C₂	semidirect
11. #11752335	C₂	semidirect
16. C₂×#6762	C₂²	semidirect
17. C₂²×C₃⋊#170	C₂²	semidirect
19. C₂×#6758	C₂²	semidirect
25. C₂×D₅⋊(C₃⋊C₈)	C₂²	semidirect
38. #91241	C₂²	semidirect
39. #91241	C₂²	semidirect
40. #91233	C₂²	semidirect
41. #91232	C₂²	semidirect
42. #91232	C₂²	semidirect
43. #91231	C₂²	semidirect
44. #91231	C₂²	semidirect
45. C₄⋊(C₃⋊#170)	C₂²	semidirect
93. D₅⋊(C₃⋊C₈)	D₄	semidirect
162. C₂²×C₃×D₅	M₁₆	semidirect
201. C₃⋊#170	C₂×D₄	semidirect
303. C₂²×C₃×C₅	C₂×M₁₆	semidirect
314. C₂×C₃×D₅	C₂×M₁₆	semidirect
386. C₂²×D₅	#208	semidirect
466. C₃×D₅	#435	semidirect
519. C₂²×C₅	C₂×#208	semidirect
529. C₂×D₅	C₂×#208	semidirect
595. C₃×C₅	C₂×#435	semidirect
612. C₂²×C₃	D₅⋊M₁₆	semidirect
632. D₅	#5011	semidirect
688. C₅	C₂×#5011	semidirect
705. C₂²	D₅⋊#208	semidirect
718. C₃	D₅⋊#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅⋊#208	2
C₂²×D₅⋊(C₃⋊C₈)	2
C₃×C₄×D₄×D₅	2
#11752432	2
D₅⋊#830	2
#11752363	2
#11752353	2
#11752352	2
D₅⋊(C₄⋊(C₃⋊C₈))	2
#11752335	2
D₅⋊#435	3
C₂×#5011	5

Subgroups — D5⋊#5011 #14414708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#5011 #14414708