Subgroups — C₃×#10617131 #14322896

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4130	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×#65712	C₂	1	4	yes	maximal, complemented
5	C₃×#65699	C₂	1	4	yes	maximal
6	C₃×#65689	C₂	1	2	yes	maximal, complemented
7	C₃×#65688	C₂	1	2	yes	maximal, complemented
8	#10617131	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
12	C₃×#4130	—	2	4	no	—
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
14	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	8	yes	—
19	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
20	C₃×C₅×#117	C₄	1	1	yes	characteristic, complemented
21	C₃×#4072	C₄	1	1	yes	characteristic, complemented
22	C₃×#4038	C₄	1	2	yes	complemented
23	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₃×#4023	C₄	1	2	yes	complemented
26	C₃×#4018	C₄	1	2	yes	complemented
27	C₃×C₄²×D₅	C₂²	1	2	yes	—
28	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	8	yes	—
29	C₃×#2317	—	5	1	no	maximal, Hall
30	C₂×#4130	C₂×C₃	1	1	yes	characteristic
31	C₂²×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
32	D₅×#117	C₂×C₃	1	1	yes	characteristic
33	#65712	C₂×C₃	1	4	yes	complemented
34	#65699	C₂×C₃	1	4	yes	—
35	#65689	C₂×C₃	1	2	yes	complemented
36	#65688	C₂×C₃	1	2	yes	complemented
37	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
39	C₂²×C₃×AGL(1,𝔽₅)	—	4	4	no	—
40	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
41	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
42	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	D₄	1	4	yes	—
48	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
49	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
53	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
54	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
55	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
56	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
57	C₃×C₄⋊AGL(1,𝔽₅)	—	4	8	no	—
58	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	complemented
60	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
62	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
63	C₃×#685	C₂×C₄	1	4	yes	—
64	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	complemented
65	C₃×#683	C₂×C₄	1	4	yes	complemented
66	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
67	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	complemented
68	C₂×C₃×#117	—	5	1	no	—
69	C₂×C₃×#117	—	5	1	no	—
70	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
71	C₃×#389	—	5	4	no	—
72	C₃×#385	—	5	4	no	—
73	C₃×#384	—	5	2	no	—
74	C₃×#382	—	5	2	no	—
75	C₂³×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
76	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
78	#4130	—	2	4	no	—
79	C₂×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
80	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
82	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
84	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	—
85	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
86	C₅×#117	C₃×C₄	1	1	yes	characteristic, complemented
87	#4072	C₃×C₄	1	1	yes	characteristic, complemented
88	#4038	C₃×C₄	1	2	yes	complemented
89	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
91	#4023	C₃×C₄	1	2	yes	complemented
92	#4018	C₃×C₄	1	2	yes	complemented
93	C₄²×D₅	C₂²×C₃	1	2	yes	—
94	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	8	yes	—
95	#2317	—	5	1	no	Sylow
96	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	2	no	—
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
101	C₂²×C₃×D₅	C₂×Q₈	1	2	yes	—
102	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
103	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
104	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
105	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
106	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
107	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
108	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
109	C₂×C₃×AGL(1,𝔽₅)	—	4	8	no	—
110	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	complemented
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	complemented
115	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
116	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
118	C₃×C₄×D₅	—	2	4	no	—
119	C₃×C₄×D₅	—	2	4	no	—
120	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	complemented
121	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	complemented
122	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
123	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
124	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
125	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
126	C₂³×C₃×C₄	—	5	1	no	—
127	C₂³×C₃×C₄	—	5	2	no	—
128	C₃×#117	—	5	1	no	—
129	C₃×#117	—	5	2	no	—
130	C₃×#117	—	5	2	no	—
131	C₃×#117	—	5	2	no	—
132	C₃×#117	—	10	4	no	—
133	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
134	C₂×C₃×C₄⋊C₄	—	5	2	no	—
135	C₂×C₃×C₄⋊C₄	—	5	1	no	—
136	C₂×C₃×C₄⋊C₄	—	5	2	no	—
137	C₂×C₃×C₄⋊C₄	—	5	1	no	—
138	C₂×C₃×C₄⋊C₄	—	5	2	no	—
139	C₂×C₃×C₄⋊C₄	—	5	8	no	—
140	C₂×C₃×C₄⋊C₄	—	10	4	no	—
141	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
142	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
143	C₂×C₃×C₄²	—	5	2	no	—
144	C₂×C₃×C₄²	—	5	2	no	—
145	C₃×#95	—	5	8	no	—
146	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
147	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
148	C₂²×AGL(1,𝔽₅)	—	4	4	no	—
149	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
150	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
151	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
152	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂×C₄×D₅	C₃×D₄	1	4	yes	—
157	C₂×C₄×D₅	C₃×Q₈	1	4	yes	—
158	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
159	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
161	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
162	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
163	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
164	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
165	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
166	C₄⋊AGL(1,𝔽₅)	—	4	8	no	—
167	C₄×AGL(1,𝔽₅)	—	2	4	no	—
168	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	complemented
169	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
170	C₄²×C₅	C₂×C₃×C₄	1	2	yes	complemented
171	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
172	#685	C₂×C₃×C₄	1	4	yes	—
173	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	complemented
174	#683	C₂×C₃×C₄	1	4	yes	complemented
175	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
176	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	complemented
177	C₂×#117	—	5	1	no	—
178	C₂×#117	—	5	1	no	—
179	C₂²×C₄⋊C₄	—	5	1	no	—
180	#389	—	5	4	no	—
181	#385	—	5	4	no	—
182	#384	—	5	2	no	—
183	#382	—	5	2	no	—
184	C₂²×C₃×C₅	—	2	2	no	—
185	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	2	no	—
188	C₂×C₃×D₅	—	2	2	no	—
189	C₂×C₃×D₅	—	2	2	no	—
190	C₂×C₃×D₅	—	2	4	no	—
191	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
192	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×D₅	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₃×D₅	H(5,𝔽₂)	1	2	yes	—
195	C₂×C₃×D₅	2₋¹⁺⁴	1	2	yes	—
196	C₃×AGL(1,𝔽₅)	—	4	2	no	—
197	C₃×AGL(1,𝔽₅)	—	4	4	no	—
198	C₃×AGL(1,𝔽₅)	—	4	2	no	—
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
201	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
202	C₃×Dic₅	—	2	4	no	—
203	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
204	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
205	C₂⁴×C₃	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	4	no	—
208	C₂²×C₃×C₄	—	5	4	no	—
209	C₂²×C₃×C₄	—	5	1	no	—
210	C₂²×C₃×C₄	—	5	1	no	—
211	C₂²×C₃×C₄	—	5	1	no	—
212	C₂²×C₃×C₄	—	5	1	no	—
213	C₂²×C₃×C₄	—	5	4	no	—
214	C₂²×C₃×C₄	—	5	2	no	—
215	C₂²×C₃×C₄	—	5	4	no	—
216	C₂²×C₃×C₄	—	5	2	no	—
217	C₂²×C₃×C₄	—	10	4	no	—
218	C₂²×C₃×C₄	—	20	4	no	—
219	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
220	C₃×C₄⋊C₄	—	5	4	no	—
221	C₃×C₄⋊C₄	—	5	2	no	—
222	C₃×C₄⋊C₄	—	10	4	no	—
223	C₃×C₄⋊C₄	—	10	4	no	—
224	C₃×C₄⋊C₄	—	10	2	no	—
225	C₃×C₄⋊C₄	—	10	2	no	—
226	C₃×C₄⋊C₄	—	20	8	no	—
227	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
228	C₃×C₂²⋊C₄	—	5	2	no	—
229	C₃×C₂²⋊C₄	—	5	4	no	—
230	C₃×C₂²⋊C₄	—	10	4	no	—
231	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
232	C₃×C₄²	—	5	4	no	—
233	C₃×C₄²	—	5	2	no	—
234	C₃×C₄²	—	10	4	no	—
235	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
236	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂²×D₅	—	2	2	no	—
238	C₂²×D₅	—	2	2	no	—
239	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
240	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
241	C₂²×D₅	C₂×C₃×Q₈	1	2	yes	—
242	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
243	C₂×AGL(1,𝔽₅)	—	2	2	no	—
244	C₂×AGL(1,𝔽₅)	—	2	2	no	—
245	C₂×AGL(1,𝔽₅)	—	2	4	no	—
246	C₂×AGL(1,𝔽₅)	—	2	4	no	—
247	C₂×AGL(1,𝔽₅)	—	2	8	no	—
248	C₂×AGL(1,𝔽₅)	—	2	4	no	—
249	C₂×AGL(1,𝔽₅)	—	4	8	no	—
250	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	complemented
251	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
252	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
254	C₂×Dic₅	C₃×C₄⋊C₄	1	4	yes	complemented
255	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
256	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₄×D₅	—	2	4	no	—
259	C₄×D₅	—	2	4	no	—
260	C₄×D₅	C₃×C₄⋊C₄	1	4	yes	complemented
261	C₄×D₅	C₃×C₄⋊C₄	1	4	yes	complemented
262	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
263	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
264	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
265	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
266	C₂³×C₄	—	5	1	no	—
267	C₂³×C₄	—	5	2	no	—
268	#117	—	5	1	no	—
269	#117	—	5	2	no	—
270	#117	—	5	2	no	—
271	#117	—	5	2	no	—
272	#117	—	10	4	no	—
273	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
274	C₂×C₄⋊C₄	—	5	2	no	—
275	C₂×C₄⋊C₄	—	5	2	no	—
276	C₂×C₄⋊C₄	—	5	2	no	—
277	C₂×C₄⋊C₄	—	5	1	no	—
278	C₂×C₄⋊C₄	—	5	1	no	—
279	C₂×C₄⋊C₄	—	5	8	no	—
280	C₂×C₄⋊C₄	—	10	4	no	—
281	C₂×C₂²⋊C₄	—	5	2	no	—
282	C₂×C₂²⋊C₄	—	5	2	no	—
283	C₂×C₄²	—	5	2	no	—
284	C₂×C₄²	—	5	2	no	—
285	#95	—	5	8	no	—
286	C₂×C₃×C₅	—	2	2	no	—
287	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₃×C₅	#520	1	2	yes	—
289	C₃×D₅	—	2	2	no	—
290	C₃×D₅	#535	1	1	yes	characteristic
291	C₃×D₅	#536	1	1	yes	characteristic
292	C₃×D₅	#544	1	2	yes	—
293	C₂³×C₃	—	5	1	no	—
294	C₂³×C₃	—	5	2	no	—
295	C₂³×C₃	—	5	2	no	—
296	C₂³×C₃	—	5	1	no	—
297	C₂³×C₃	—	10	2	no	—
298	C₂³×C₃	—	10	2	no	—
299	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₂×C₃×C₄	—	5	4	no	—
301	C₂×C₃×C₄	—	5	1	no	—
302	C₂×C₃×C₄	—	5	1	no	—
303	C₂×C₃×C₄	—	5	4	no	—
304	C₂×C₃×C₄	—	5	4	no	—
305	C₂×C₃×C₄	—	5	2	no	—
306	C₂×C₃×C₄	—	5	2	no	—
307	C₂×C₃×C₄	—	5	2	no	—
308	C₂×C₃×C₄	—	5	2	no	—
309	C₂×C₃×C₄	—	5	4	no	—
310	C₂×C₃×C₄	—	10	4	no	—
311	C₂×C₃×C₄	—	10	4	no	—
312	C₂×C₃×C₄	—	10	2	no	—
313	C₂×C₃×C₄	—	10	2	no	—
314	C₂×C₃×C₄	—	10	4	no	—
315	C₂×C₃×C₄	—	10	4	no	—
316	C₂×C₃×C₄	—	10	8	no	—
317	C₂×C₃×C₄	—	10	4	no	—
318	C₂×C₃×C₄	—	20	8	no	—
319	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	4	yes	complemented
320	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	4	yes	—
321	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
323	C₂²×C₅	—	2	2	no	—
324	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
325	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
326	C₂×D₅	—	2	2	no	—
327	C₂×D₅	—	2	2	no	—
328	C₂×D₅	—	2	2	no	—
329	C₂×D₅	—	2	4	no	—
330	C₂×D₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
331	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
332	C₂×D₅	C₂²×C₃×Q₈	1	1	yes	characteristic
333	C₂×D₅	C₃×H(5,𝔽₂)	1	2	yes	—
334	C₂×D₅	C₃×2₋¹⁺⁴	1	2	yes	—
335	AGL(1,𝔽₅)	—	4	2	no	—
336	AGL(1,𝔽₅)	—	4	4	no	—
337	AGL(1,𝔽₅)	—	4	2	no	—
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
340	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
341	Dic₅	—	2	4	no	—
342	Dic₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
343	Dic₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
344	C₂⁴	—	5	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	—	5	4	no	—
347	C₂²×C₄	—	5	4	no	—
348	C₂²×C₄	—	5	1	no	—
349	C₂²×C₄	—	5	1	no	—
350	C₂²×C₄	—	5	1	no	—
351	C₂²×C₄	—	5	1	no	—
352	C₂²×C₄	—	5	4	no	—
353	C₂²×C₄	—	5	2	no	—
354	C₂²×C₄	—	5	4	no	—
355	C₂²×C₄	—	5	2	no	—
356	C₂²×C₄	—	10	4	no	—
357	C₂²×C₄	—	20	4	no	—
358	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₄⋊C₄	—	5	4	no	—
360	C₄⋊C₄	—	5	2	no	—
361	C₄⋊C₄	—	10	4	no	—
362	C₄⋊C₄	—	10	4	no	—
363	C₄⋊C₄	—	10	2	no	—
364	C₄⋊C₄	—	10	2	no	—
365	C₄⋊C₄	—	20	8	no	—
366	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
367	C₂²⋊C₄	—	5	2	no	—
368	C₂²⋊C₄	—	5	4	no	—
369	C₂²⋊C₄	—	10	4	no	—
370	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
371	C₄²	—	5	4	no	—
372	C₄²	—	5	2	no	—
373	C₄²	—	10	4	no	—
374	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
375	C₃×C₅	#2317	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	5	1	no	—
378	C₂²×C₃	—	5	1	no	—
379	C₂²×C₃	—	5	2	no	—
380	C₂²×C₃	—	5	2	no	—
381	C₂²×C₃	—	5	2	no	—
382	C₂²×C₃	—	10	2	no	—
383	C₂²×C₃	—	10	2	no	—
384	C₂²×C₃	—	10	4	no	—
385	C₂²×C₃	—	10	2	no	—
386	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
387	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
388	C₃×C₄	—	2	4	no	—
389	C₃×C₄	—	5	2	no	—
390	C₃×C₄	—	5	2	no	—
391	C₃×C₄	—	10	4	no	—
392	C₃×C₄	—	20	2	no	—
393	C₃×C₄	—	20	2	no	—
394	C₃×C₄	—	20	4	no	—
395	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
396	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
397	C₂×C₅	—	2	2	no	—
398	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
399	C₂×C₅	C₃×#520	1	2	yes	—
400	D₅	—	2	2	no	—
401	D₅	C₃×#535	1	1	yes	characteristic
402	D₅	C₃×#536	1	1	yes	characteristic
403	D₅	C₃×#544	1	2	yes	—
404	C₂³	—	5	1	no	—
405	C₂³	—	5	2	no	—
406	C₂³	—	5	2	no	—
407	C₂³	—	5	1	no	—
408	C₂³	—	10	2	no	—
409	C₂³	—	10	2	no	—
410	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₂×C₄	—	5	4	no	—
412	C₂×C₄	—	5	1	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	5	2	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	5	4	no	—
417	C₂×C₄	—	5	4	no	—
418	C₂×C₄	—	5	2	no	—
419	C₂×C₄	—	5	2	no	—
420	C₂×C₄	—	5	4	no	—
421	C₂×C₄	—	10	4	no	—
422	C₂×C₄	—	10	4	no	—
423	C₂×C₄	—	10	2	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	10	4	no	—
426	C₂×C₄	—	10	4	no	—
427	C₂×C₄	—	10	8	no	—
428	C₂×C₄	—	10	4	no	—
429	C₂×C₄	—	20	8	no	—
430	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	4	yes	complemented
431	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
432	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
434	C₂×C₃	—	2	2	no	—
435	C₂×C₃	—	5	1	no	—
436	C₂×C₃	—	5	1	no	—
437	C₂×C₃	—	5	2	no	—
438	C₂×C₃	—	10	2	no	—
439	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₂×C₃	#66266	1	2	yes	—
441	C₅	C₃×#2317	1	1	yes	characteristic, complemented, Sylow
442	C₂²	—	2	2	no	—
443	C₂²	—	5	1	no	—
444	C₂²	—	5	1	no	—
445	C₂²	—	5	2	no	—
446	C₂²	—	5	2	no	—
447	C₂²	—	5	2	no	—
448	C₂²	—	10	2	no	—
449	C₂²	—	10	2	no	—
450	C₂²	—	10	4	no	—
451	C₂²	—	10	2	no	—
452	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
453	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	5	2	no	—
456	C₄	—	5	2	no	—
457	C₄	—	10	4	no	—
458	C₄	—	20	4	no	—
459	C₄	—	20	2	no	—
460	C₄	—	20	2	no	—
461	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
462	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
463	C₃	#10617131	1	1	yes	characteristic, direct product factor, Sylow
464	C₂	—	2	2	no	—
465	C₂	—	5	1	no	—
466	C₂	—	5	1	no	—
467	C₂	—	5	2	no	—
468	C₂	—	10	2	no	—
469	C₂	C₂²×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
470	C₂	C₃×#66266	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#117	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×#117	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2317
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
4. C₃×#65712	C₂	semidirect
6. C₃×#65689	C₂	semidirect
7. C₃×#65688	C₂	semidirect
8. #10617131	C₃	direct (N × H)
20. C₃×C₅×#117	C₄	semidirect
21. C₃×#4072	C₄	semidirect
22. C₃×#4038	C₄	semidirect
25. C₃×#4023	C₄	semidirect
26. C₃×#4018	C₄	semidirect
33. #65712	C₂×C₃	semidirect
35. #65689	C₂×C₃	semidirect
36. #65688	C₂×C₃	semidirect
59. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
61. C₃×C₄²×C₅	C₂×C₄	semidirect
64. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
65. C₃×#683	C₂×C₄	semidirect
66. C₃×C₄×Dic₅	C₂×C₄	semidirect
67. C₃×C₄×Dic₅	C₂×C₄	semidirect
86. C₅×#117	C₃×C₄	semidirect
87. #4072	C₃×C₄	semidirect
88. #4038	C₃×C₄	semidirect
91. #4023	C₃×C₄	semidirect
92. #4018	C₃×C₄	semidirect
110. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
114. C₂×C₃×Dic₅	C₄⋊C₄	semidirect
120. C₃×C₄×D₅	C₄⋊C₄	semidirect
121. C₃×C₄×D₅	C₄⋊C₄	semidirect
133. C₃×#117	AGL(1,𝔽₅)	semidirect
168. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
170. C₄²×C₅	C₂×C₃×C₄	semidirect
173. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
174. #683	C₂×C₃×C₄	semidirect
175. C₄×Dic₅	C₂×C₃×C₄	semidirect
176. C₄×Dic₅	C₂×C₃×C₄	semidirect
227. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
235. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
250. C₂×C₄×C₅	C₃×C₄⋊C₄	semidirect
254. C₂×Dic₅	C₃×C₄⋊C₄	semidirect
260. C₄×D₅	C₃×C₄⋊C₄	semidirect
261. C₄×D₅	C₃×C₄⋊C₄	semidirect
273. #117	C₃×AGL(1,𝔽₅)	semidirect
319. C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	semidirect
366. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
374. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
375. C₃×C₅	#2317	semidirect
430. C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	semidirect
441. C₅	C₃×#2317	semidirect
463. C₃	#10617131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4130	2
C₂²×C₃×C₄⋊AGL(1,𝔽₅)	2
C₃×D₅×#117	2
C₃×#65712	2
C₃×#65699	2
C₃×#65689	2
C₃×#65688	2
#10617131	3
C₃×#2317	5

Subgroups — C3×#10617131 #14322896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617131 #14322896