Subgroups — C₃×#10617346 #14329914

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×#65712	C₂	1	1	yes	maximal, characteristic
3	C₃×#65712	C₂	1	1	yes	maximal, characteristic
4	C₃×#65712	C₂	1	2	yes	maximal
5	C₃×#65711	C₂	1	2	yes	maximal
6	C₃×#65711	C₂	1	2	yes	maximal
7	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
10	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
12	#10617346	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
22	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
23	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
24	C₃×C₅×#125	C₄	1	1	yes	characteristic, complemented
25	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₃×#4036	C₄	1	1	yes	characteristic, complemented
30	C₃×#4036	C₄	1	1	yes	characteristic, complemented
31	C₃×#4035	C₄	1	2	yes	complemented
32	C₃×#4035	C₄	1	2	yes	complemented
33	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
34	C₃×#4016	C₄	1	1	yes	characteristic, complemented
35	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
38	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
39	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
40	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
41	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
42	C₃×#2370	—	5	1	no	maximal, Hall
43	D₅×#125	C₂×C₃	1	1	yes	characteristic
44	#65712	C₂×C₃	1	1	yes	characteristic
45	#65712	C₂×C₃	1	1	yes	characteristic
46	#65712	C₂×C₃	1	2	yes	—
47	#65711	C₂×C₃	1	2	yes	—
48	#65711	C₂×C₃	1	2	yes	—
49	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
50	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
51	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
52	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
53	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
54	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
55	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
56	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
57	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
58	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
59	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
62	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
63	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
65	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
66	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
67	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
68	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
69	C₃×C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
70	C₃×C₄⋊AGL(1,𝔽₅)	Q₈	1	4	yes	—
71	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
72	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
73	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
74	C₃×C₄×AGL(1,𝔽₅)	—	4	2	no	—
75	C₃×C₄×AGL(1,𝔽₅)	—	4	2	no	—
76	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
78	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
84	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
85	C₃×#683	C₂×C₄	1	2	yes	—
86	C₃×#683	C₂×C₄	1	2	yes	—
87	C₃×#683	C₂×C₄	1	2	yes	—
88	C₃×#683	C₂×C₄	1	2	yes	—
89	C₃×#683	C₂×C₄	1	2	yes	—
90	C₃×#683	C₂×C₄	1	2	yes	—
91	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
93	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×#125	—	5	1	no	—
95	C₃×#389	—	5	1	no	—
96	C₃×#389	—	5	2	no	—
97	C₃×#389	—	5	1	no	—
98	C₃×#387	—	5	2	no	—
99	C₃×#387	—	5	2	no	—
100	C₃×C₄×C₄⋊C₄	—	5	1	no	—
101	C₃×C₄×C₄⋊C₄	—	5	1	no	—
102	C₃×C₄×C₄⋊C₄	—	5	2	no	—
103	C₃×C₄×C₄⋊C₄	—	5	1	no	—
104	C₃×C₄×C₄⋊C₄	—	5	1	no	—
105	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
109	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
110	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
114	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
115	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
116	C₅×#125	C₃×C₄	1	1	yes	characteristic, complemented
117	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
118	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
121	#4036	C₃×C₄	1	1	yes	characteristic, complemented
122	#4036	C₃×C₄	1	1	yes	characteristic, complemented
123	#4035	C₃×C₄	1	2	yes	complemented
124	#4035	C₃×C₄	1	2	yes	complemented
125	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
126	#4016	C₃×C₄	1	1	yes	characteristic, complemented
127	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
130	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
131	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
132	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
133	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
134	#2370	—	5	1	no	Sylow
135	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
137	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
138	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
139	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
140	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
141	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
142	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
143	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
144	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
145	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
146	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
147	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
148	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
149	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
150	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
151	C₂×C₃×AGL(1,𝔽₅)	C₂×Q₈	1	4	yes	—
152	C₂×C₃×AGL(1,𝔽₅)	#41	1	2	yes	—
153	C₂×C₃×AGL(1,𝔽₅)	#41	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
157	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
162	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
163	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	—	2	1	no	—
166	C₃×C₄×D₅	—	2	2	no	—
167	C₃×C₄×D₅	—	2	1	no	—
168	C₃×C₄×D₅	—	2	1	no	—
169	C₃×C₄×D₅	—	2	2	no	—
170	C₃×C₄×D₅	—	2	1	no	—
171	C₃×C₄×D₅	—	2	2	no	—
172	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
173	C₃×C₄×D₅	#41	1	2	yes	—
174	C₃×#125	—	5	2	no	—
175	C₃×#125	—	5	2	no	—
176	C₃×#125	—	5	1	no	—
177	C₃×#125	—	5	1	no	—
178	C₃×#125	—	5	1	no	—
179	C₃×#125	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
180	C₂×C₃×C₄⋊C₄	—	5	1	no	—
181	C₂×C₃×C₄⋊C₄	—	5	2	no	—
182	C₂×C₃×C₄⋊C₄	—	5	1	no	—
183	C₂×C₃×C₄⋊C₄	—	5	1	no	—
184	C₂×C₃×C₄⋊C₄	—	5	2	no	—
185	C₂×C₃×C₄⋊C₄	—	5	1	no	—
186	C₂×C₃×C₄⋊C₄	—	5	1	no	—
187	C₂×C₃×C₄⋊C₄	—	5	1	no	—
188	C₂×C₃×C₄⋊C₄	—	5	2	no	—
189	C₂×C₃×C₄⋊C₄	—	5	2	no	—
190	C₂×C₃×C₄²	—	5	1	no	—
191	C₂×C₃×C₄²	—	5	2	no	—
192	C₂×C₃×C₄²	—	5	1	no	—
193	C₂×C₃×C₄²	—	5	1	no	—
194	C₂×C₃×C₄²	—	5	2	no	—
195	C₂×C₃×C₄²	—	5	2	no	—
196	C₃×#95	—	5	1	no	—
197	C₃×#95	—	5	2	no	—
198	C₃×#95	—	5	1	no	—
199	C₃×#95	—	5	2	no	—
200	C₃×#95	—	5	2	no	—
201	C₃×#95	—	5	2	no	—
202	C₃×#95	—	5	2	no	—
203	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
204	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
205	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
206	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
207	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
208	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
211	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
212	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
213	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
214	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
215	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
216	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
217	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
218	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
219	C₄⋊AGL(1,𝔽₅)	C₃×Q₈	1	4	yes	—
220	C₄×AGL(1,𝔽₅)	—	2	4	no	—
221	C₄×AGL(1,𝔽₅)	—	2	2	no	—
222	C₄×AGL(1,𝔽₅)	—	2	2	no	—
223	C₄×AGL(1,𝔽₅)	—	4	2	no	—
224	C₄×AGL(1,𝔽₅)	—	4	2	no	—
225	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
226	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
227	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
228	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
229	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
230	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
231	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
232	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
233	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
234	#683	C₂×C₃×C₄	1	2	yes	—
235	#683	C₂×C₃×C₄	1	2	yes	—
236	#683	C₂×C₃×C₄	1	2	yes	—
237	#683	C₂×C₃×C₄	1	2	yes	—
238	#683	C₂×C₃×C₄	1	2	yes	—
239	#683	C₂×C₃×C₄	1	2	yes	—
240	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
241	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
242	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
243	C₂×#125	—	5	1	no	—
244	#389	—	5	1	no	—
245	#389	—	5	2	no	—
246	#389	—	5	1	no	—
247	#387	—	5	2	no	—
248	#387	—	5	2	no	—
249	C₄×C₄⋊C₄	—	5	1	no	—
250	C₄×C₄⋊C₄	—	5	1	no	—
251	C₄×C₄⋊C₄	—	5	2	no	—
252	C₄×C₄⋊C₄	—	5	1	no	—
253	C₄×C₄⋊C₄	—	5	1	no	—
254	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₃×D₅	C₂²×Q₈	1	1	yes	characteristic
256	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
257	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
258	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
259	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₃×D₅	2₋¹⁺⁴	1	1	yes	characteristic
261	C₃×AGL(1,𝔽₅)	—	2	2	no	—
262	C₃×AGL(1,𝔽₅)	—	2	2	no	—
263	C₃×AGL(1,𝔽₅)	—	2	4	no	—
264	C₃×AGL(1,𝔽₅)	—	4	1	no	—
265	C₃×AGL(1,𝔽₅)	—	4	1	no	—
266	C₃×AGL(1,𝔽₅)	—	4	2	no	—
267	C₃×C₄×C₅	—	2	2	no	—
268	C₃×C₄×C₅	—	2	1	no	—
269	C₃×C₄×C₅	—	2	1	no	—
270	C₃×C₄×C₅	—	2	2	no	—
271	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
272	C₃×Dic₅	—	2	2	no	—
273	C₃×Dic₅	—	2	1	no	—
274	C₃×Dic₅	—	2	1	no	—
275	C₃×Dic₅	—	2	2	no	—
276	C₃×Dic₅	C₄×Q₈	1	2	yes	—
277	C₂²×C₃×C₄	—	5	1	no	—
278	C₂²×C₃×C₄	—	5	2	no	—
279	C₂²×C₃×C₄	—	5	1	no	—
280	C₂²×C₃×C₄	—	5	1	no	—
281	C₂²×C₃×C₄	—	5	1	no	—
282	C₂²×C₃×C₄	—	5	1	no	—
283	C₂²×C₃×C₄	—	5	2	no	—
284	C₂²×C₃×C₄	—	5	2	no	—
285	C₂²×C₃×C₄	—	5	1	no	—
286	C₂²×C₃×C₄	—	5	1	no	—
287	C₂²×C₃×C₄	—	5	2	no	—
288	C₃×C₄⋊C₄	—	5	4	no	—
289	C₃×C₄⋊C₄	—	5	2	no	—
290	C₃×C₄⋊C₄	—	5	2	no	—
291	C₃×C₄⋊C₄	—	5	2	no	—
292	C₃×C₄⋊C₄	—	5	2	no	—
293	C₃×C₄⋊C₄	—	5	2	no	—
294	C₃×C₄⋊C₄	—	5	2	no	—
295	C₃×C₄⋊C₄	—	5	2	no	—
296	C₃×C₄⋊C₄	—	5	2	no	—
297	C₃×C₄⋊C₄	—	5	1	no	—
298	C₃×C₄⋊C₄	—	5	1	no	—
299	C₃×C₄⋊C₄	—	10	2	no	—
300	C₃×C₄⋊C₄	—	10	2	no	—
301	C₃×C₄⋊C₄	—	10	2	no	—
302	C₃×C₄⋊C₄	—	10	4	no	—
303	C₃×C₄⋊C₄	—	20	2	no	—
304	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
305	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
306	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₃×C₄²	—	5	1	no	—
309	C₃×C₄²	—	5	1	no	—
310	C₃×C₄²	—	5	1	no	—
311	C₃×C₄²	—	10	2	no	—
312	C₃×C₄²	—	10	2	no	—
313	C₃×C₄²	—	10	4	no	—
314	C₃×C₄²	—	20	2	no	—
315	C₃×C₄²	—	20	2	no	—
316	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
318	C₂×AGL(1,𝔽₅)	—	2	1	no	—
319	C₂×AGL(1,𝔽₅)	—	2	1	no	—
320	C₂×AGL(1,𝔽₅)	—	2	2	no	—
321	C₂×AGL(1,𝔽₅)	—	2	1	no	—
322	C₂×AGL(1,𝔽₅)	—	2	2	no	—
323	C₂×AGL(1,𝔽₅)	—	2	1	no	—
324	C₂×AGL(1,𝔽₅)	—	2	1	no	—
325	C₂×AGL(1,𝔽₅)	—	2	1	no	—
326	C₂×AGL(1,𝔽₅)	—	2	1	no	—
327	C₂×AGL(1,𝔽₅)	—	2	2	no	—
328	C₂×AGL(1,𝔽₅)	—	2	1	no	—
329	C₂×AGL(1,𝔽₅)	—	2	2	no	—
330	C₂×AGL(1,𝔽₅)	—	2	2	no	—
331	C₂×AGL(1,𝔽₅)	—	2	1	no	—
332	C₂×AGL(1,𝔽₅)	—	2	1	no	—
333	C₂×AGL(1,𝔽₅)	C₂×C₃×Q₈	1	4	yes	—
334	C₂×AGL(1,𝔽₅)	C₃×#41	1	2	yes	—
335	C₂×AGL(1,𝔽₅)	C₃×#41	1	2	yes	—
336	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
339	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
340	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
341	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
342	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
343	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
344	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
345	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
346	C₄×D₅	—	2	2	no	—
347	C₄×D₅	—	2	1	no	—
348	C₄×D₅	—	2	2	no	—
349	C₄×D₅	—	2	1	no	—
350	C₄×D₅	—	2	1	no	—
351	C₄×D₅	—	2	2	no	—
352	C₄×D₅	—	2	1	no	—
353	C₄×D₅	—	2	2	no	—
354	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
355	C₄×D₅	C₃×#41	1	2	yes	—
356	#125	—	5	2	no	—
357	#125	—	5	2	no	—
358	#125	—	5	1	no	—
359	#125	—	5	1	no	—
360	#125	—	5	1	no	—
361	#125	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
362	C₂×C₄⋊C₄	—	5	1	no	—
363	C₂×C₄⋊C₄	—	5	2	no	—
364	C₂×C₄⋊C₄	—	5	1	no	—
365	C₂×C₄⋊C₄	—	5	1	no	—
366	C₂×C₄⋊C₄	—	5	2	no	—
367	C₂×C₄⋊C₄	—	5	1	no	—
368	C₂×C₄⋊C₄	—	5	1	no	—
369	C₂×C₄⋊C₄	—	5	1	no	—
370	C₂×C₄⋊C₄	—	5	2	no	—
371	C₂×C₄⋊C₄	—	5	2	no	—
372	C₂×C₄²	—	5	1	no	—
373	C₂×C₄²	—	5	2	no	—
374	C₂×C₄²	—	5	1	no	—
375	C₂×C₄²	—	5	1	no	—
376	C₂×C₄²	—	5	2	no	—
377	C₂×C₄²	—	5	2	no	—
378	#95	—	5	1	no	—
379	#95	—	5	2	no	—
380	#95	—	5	1	no	—
381	#95	—	5	2	no	—
382	#95	—	5	2	no	—
383	#95	—	5	2	no	—
384	#95	—	5	2	no	—
385	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
386	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
387	C₂×C₃×C₅	#520	1	1	yes	characteristic
388	C₃×D₅	#552	1	1	yes	characteristic
389	C₃×D₅	#553	1	1	yes	characteristic
390	C₃×D₅	#554	1	1	yes	characteristic
391	C₃×D₅	#557	1	1	yes	characteristic
392	C₂³×C₃	—	5	1	no	—
393	C₂×C₃×C₄	—	5	1	no	—
394	C₂×C₃×C₄	—	5	2	no	—
395	C₂×C₃×C₄	—	5	2	no	—
396	C₂×C₃×C₄	—	5	4	no	—
397	C₂×C₃×C₄	—	5	2	no	—
398	C₂×C₃×C₄	—	5	2	no	—
399	C₂×C₃×C₄	—	5	1	no	—
400	C₂×C₃×C₄	—	5	1	no	—
401	C₂×C₃×C₄	—	5	2	no	—
402	C₂×C₃×C₄	—	5	2	no	—
403	C₂×C₃×C₄	—	10	2	no	—
404	C₂×C₃×C₄	—	10	1	no	—
405	C₂×C₃×C₄	—	10	2	no	—
406	C₂×C₃×C₄	—	10	2	no	—
407	C₂×C₃×C₄	—	10	1	no	—
408	C₂×C₃×C₄	—	10	1	no	—
409	C₂×C₃×C₄	—	10	1	no	—
410	C₂×C₃×C₄	—	10	2	no	—
411	C₂×C₃×C₄	—	10	1	no	—
412	C₂×C₃×C₄	—	10	1	no	—
413	C₂×C₃×C₄	—	10	2	no	—
414	C₂×C₃×C₄	—	10	2	no	—
415	C₂×C₃×C₄	—	10	1	no	—
416	C₂×C₃×C₄	—	10	1	no	—
417	C₂×C₃×C₄	—	10	1	no	—
418	C₂×C₃×C₄	—	10	1	no	—
419	C₂×C₃×C₄	—	10	2	no	—
420	C₂×C₃×C₄	—	10	2	no	—
421	C₂×C₃×C₄	—	10	1	no	—
422	C₂×C₃×C₄	—	10	1	no	—
423	C₂×C₃×C₄	—	10	2	no	—
424	C₂×C₃×C₄	—	10	1	no	—
425	C₂×C₃×C₄	—	10	1	no	—
426	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
429	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
430	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
431	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
432	C₂×D₅	C₂²×C₃×Q₈	1	1	yes	characteristic
433	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
434	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
435	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
436	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂×D₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
438	AGL(1,𝔽₅)	—	2	2	no	—
439	AGL(1,𝔽₅)	—	2	2	no	—
440	AGL(1,𝔽₅)	—	2	4	no	—
441	AGL(1,𝔽₅)	—	4	1	no	—
442	AGL(1,𝔽₅)	—	4	1	no	—
443	AGL(1,𝔽₅)	—	4	2	no	—
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	—	2	1	no	—
447	C₄×C₅	—	2	2	no	—
448	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
449	Dic₅	—	2	2	no	—
450	Dic₅	—	2	1	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	—	2	2	no	—
453	Dic₅	C₃×C₄×Q₈	1	2	yes	—
454	C₂²×C₄	—	5	1	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	5	2	no	—
457	C₂²×C₄	—	5	1	no	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	1	no	—
460	C₂²×C₄	—	5	2	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	1	no	—
463	C₂²×C₄	—	5	1	no	—
464	C₂²×C₄	—	5	2	no	—
465	C₄⋊C₄	—	5	4	no	—
466	C₄⋊C₄	—	5	2	no	—
467	C₄⋊C₄	—	5	2	no	—
468	C₄⋊C₄	—	5	2	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₄⋊C₄	—	5	2	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	—	5	2	no	—
474	C₄⋊C₄	—	5	1	no	—
475	C₄⋊C₄	—	5	1	no	—
476	C₄⋊C₄	—	10	2	no	—
477	C₄⋊C₄	—	10	2	no	—
478	C₄⋊C₄	—	10	2	no	—
479	C₄⋊C₄	—	10	4	no	—
480	C₄⋊C₄	—	20	2	no	—
481	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
482	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
483	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
484	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
485	C₄²	—	5	1	no	—
486	C₄²	—	5	1	no	—
487	C₄²	—	5	1	no	—
488	C₄²	—	10	2	no	—
489	C₄²	—	10	2	no	—
490	C₄²	—	10	4	no	—
491	C₄²	—	20	2	no	—
492	C₄²	—	20	2	no	—
493	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
494	C₃×C₅	#2370	1	1	yes	characteristic, complemented, Hall
495	C₂²×C₃	—	5	1	no	—
496	C₂²×C₃	—	5	1	no	—
497	C₂²×C₃	—	5	1	no	—
498	C₂²×C₃	—	5	1	no	—
499	C₂²×C₃	—	5	1	no	—
500	C₂²×C₃	—	5	1	no	—
501	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	5	2	no	—
507	C₃×C₄	—	10	4	no	—
508	C₃×C₄	—	10	2	no	—
509	C₃×C₄	—	10	2	no	—
510	C₃×C₄	—	10	1	no	—
511	C₃×C₄	—	10	2	no	—
512	C₃×C₄	—	10	1	no	—
513	C₃×C₄	—	10	2	no	—
514	C₃×C₄	—	20	1	no	—
515	C₃×C₄	—	20	2	no	—
516	C₃×C₄	—	20	1	no	—
517	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	2	yes	—
518	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
519	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
520	C₂×C₅	C₃×#520	1	1	yes	characteristic
521	D₅	C₃×#552	1	1	yes	characteristic
522	D₅	C₃×#553	1	1	yes	characteristic
523	D₅	C₃×#554	1	1	yes	characteristic
524	D₅	C₃×#557	1	1	yes	characteristic
525	C₂³	—	5	1	no	—
526	C₂×C₄	—	5	1	no	—
527	C₂×C₄	—	5	2	no	—
528	C₂×C₄	—	5	2	no	—
529	C₂×C₄	—	5	2	no	—
530	C₂×C₄	—	5	4	no	—
531	C₂×C₄	—	5	2	no	—
532	C₂×C₄	—	5	1	no	—
533	C₂×C₄	—	5	1	no	—
534	C₂×C₄	—	5	2	no	—
535	C₂×C₄	—	5	2	no	—
536	C₂×C₄	—	10	2	no	—
537	C₂×C₄	—	10	1	no	—
538	C₂×C₄	—	10	2	no	—
539	C₂×C₄	—	10	2	no	—
540	C₂×C₄	—	10	1	no	—
541	C₂×C₄	—	10	1	no	—
542	C₂×C₄	—	10	1	no	—
543	C₂×C₄	—	10	2	no	—
544	C₂×C₄	—	10	1	no	—
545	C₂×C₄	—	10	1	no	—
546	C₂×C₄	—	10	2	no	—
547	C₂×C₄	—	10	2	no	—
548	C₂×C₄	—	10	1	no	—
549	C₂×C₄	—	10	1	no	—
550	C₂×C₄	—	10	1	no	—
551	C₂×C₄	—	10	1	no	—
552	C₂×C₄	—	10	2	no	—
553	C₂×C₄	—	10	2	no	—
554	C₂×C₄	—	10	1	no	—
555	C₂×C₄	—	10	1	no	—
556	C₂×C₄	—	10	2	no	—
557	C₂×C₄	—	10	1	no	—
558	C₂×C₄	—	10	1	no	—
559	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
560	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
561	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
562	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
563	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
564	C₂×C₃	—	5	1	no	—
565	C₂×C₃	—	5	1	no	—
566	C₂×C₃	—	5	1	no	—
567	C₂×C₃	—	5	1	no	—
568	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
569	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
570	C₂×C₃	#66266	1	1	yes	characteristic
571	C₅	C₃×#2370	1	1	yes	characteristic, complemented, Sylow
572	C₂²	—	5	1	no	—
573	C₂²	—	5	1	no	—
574	C₂²	—	5	1	no	—
575	C₂²	—	5	1	no	—
576	C₂²	—	5	1	no	—
577	C₂²	—	5	1	no	—
578	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
579	C₄	—	2	2	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	2	no	—
583	C₄	—	5	2	no	—
584	C₄	—	10	4	no	—
585	C₄	—	10	2	no	—
586	C₄	—	10	2	no	—
587	C₄	—	10	1	no	—
588	C₄	—	10	2	no	—
589	C₄	—	10	1	no	—
590	C₄	—	10	2	no	—
591	C₄	—	20	1	no	—
592	C₄	—	20	2	no	—
593	C₄	—	20	1	no	—
594	C₄	C₃×Q₈×AGL(1,𝔽₅)	1	2	yes	—
595	C₃	#10617346	1	1	yes	characteristic, direct product factor, Sylow
596	C₂	—	5	1	no	—
597	C₂	—	5	1	no	—
598	C₂	—	5	1	no	—
599	C₂	—	5	1	no	—
600	C₂	C₂×C₃×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
601	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic
602	C₂	C₃×#66266	1	1	yes	characteristic

	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×#125	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂⁴
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×#125	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2370
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#125

Complements

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

N	H ≅ G/N	type
12. #10617346	C₃	direct (N × H)
24. C₃×C₅×#125	C₄	semidirect
29. C₃×#4036	C₄	semidirect
30. C₃×#4036	C₄	semidirect
31. C₃×#4035	C₄	semidirect
32. C₃×#4035	C₄	semidirect
34. C₃×#4016	C₄	semidirect
116. C₅×#125	C₃×C₄	semidirect
121. #4036	C₃×C₄	semidirect
122. #4036	C₃×C₄	semidirect
123. #4035	C₃×C₄	semidirect
124. #4035	C₃×C₄	semidirect
126. #4016	C₃×C₄	semidirect
179. C₃×#125	AGL(1,𝔽₅)	semidirect
361. #125	C₃×AGL(1,𝔽₅)	semidirect
494. C₃×C₅	#2370	semidirect
571. C₅	C₃×#2370	semidirect
595. C₃	#10617346	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×#125	2
C₃×#65712	2
C₃×#65711	2
C₃×C₄⋊C₄×AGL(1,𝔽₅)	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
#10617346	3
C₃×#2370	5

Subgroups — C3×#10617346 #14329914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617346 #14329914