Subgroups — C₃×#10617210 #14323261

Order 1920.

888 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	C₂	1	2	yes	maximal
3	C₃×#65712	C₂	1	2	yes	maximal
4	C₃×#65711	C₂	1	4	yes	maximal
5	C₃×#65690	C₂	1	2	yes	maximal
6	C₃×#65689	C₂	1	2	yes	maximal
7	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
8	C₃×#65686	C₂	1	1	yes	maximal, characteristic
9	#10617210	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
12	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
13	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
15	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
16	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic, complemented
17	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃×#4033	C₄	1	2	yes	complemented
20	C₃×#4033	C₄	1	1	yes	characteristic, complemented
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₂²	1	2	yes	—
23	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic, complemented
24	C₃×C₄×Dic₁₀	C₄	1	2	yes	complemented
25	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
28	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
29	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
30	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
31	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
32	C₃×#2320	—	5	1	no	maximal, Hall
33	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic
34	(C₂×AGL(1,𝔽₅))⋊Q₈	C₂×C₃	1	2	yes	—
35	#65712	C₂×C₃	1	2	yes	—
36	#65711	C₂×C₃	1	4	yes	—
37	#65690	C₂×C₃	1	2	yes	—
38	#65689	C₂×C₃	1	2	yes	—
39	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
40	#65686	C₂×C₃	1	1	yes	characteristic
41	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
42	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
43	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₃×Q₈×D₅	—	2	4	no	—
46	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
48	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
49	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
53	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
54	C₃×C₄⋊AGL(1,𝔽₅)	—	4	4	no	—
55	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
56	C₃×C₄×AGL(1,𝔽₅)	—	4	2	no	—
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
62	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
63	C₃×#683	C₂×C₄	1	2	yes	—
64	C₃×#683	C₂×C₄	1	2	yes	—
65	C₃×#683	C₂×C₄	1	2	yes	—
66	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
68	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
69	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
71	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×C₄×Q₈	—	5	1	no	—
73	C₃×#391	—	5	2	no	—
74	C₃×#389	—	5	2	no	—
75	C₃×#387	—	5	4	no	—
76	C₃×#383	—	5	2	no	—
77	C₃×#382	—	5	2	no	—
78	C₃×C₄×C₄⋊C₄	—	5	1	no	—
79	C₃×#376	—	5	1	no	—
80	C₂×Q₈×D₅	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	4	yes	—
83	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
84	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
85	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
86	Q₈×Dic₅	C₃×C₄	1	1	yes	characteristic, complemented
87	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	#4033	C₃×C₄	1	1	yes	characteristic, complemented
90	#4033	C₃×C₄	1	2	yes	complemented
91	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
92	C₄²×D₅	C₂²×C₃	1	2	yes	—
93	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic, complemented
94	C₄×Dic₁₀	C₃×C₄	1	2	yes	complemented
95	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
98	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
99	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
100	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
101	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
102	#2320	—	5	1	no	Sylow
103	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
104	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
105	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
106	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
107	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
108	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
109	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
110	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
111	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
112	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
123	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
124	C₃×C₄×D₅	—	2	4	no	—
125	C₃×C₄×D₅	—	2	1	no	—
126	C₃×C₄×D₅	—	2	2	no	—
127	C₃×C₄×D₅	—	2	2	no	—
128	C₃×C₄×D₅	—	2	1	no	—
129	C₃×C₄×D₅	—	2	2	no	—
130	C₃×C₄×D₅	#41	1	4	yes	—
131	C₃×Dic₁₀	—	2	2	no	—
132	C₃×Dic₁₀	—	2	4	no	—
133	C₂²×C₃×Q₈	—	5	1	no	—
134	C₃×C₄×Q₈	—	5	1	no	—
135	C₃×C₄×Q₈	—	5	2	no	—
136	C₃×C₄×Q₈	—	5	1	no	—
137	C₃×C₄×Q₈	—	5	2	no	—
138	C₃×C₄×Q₈	—	5	1	no	—
139	C₃×C₄×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
140	C₂×C₃×C₄⋊C₄	—	5	2	no	—
141	C₂×C₃×C₄⋊C₄	—	5	1	no	—
142	C₂×C₃×C₄⋊C₄	—	5	2	no	—
143	C₂×C₃×C₄⋊C₄	—	5	4	no	—
144	C₂×C₃×C₄²	—	5	1	no	—
145	C₂×C₃×C₄²	—	5	2	no	—
146	C₂×C₃×C₄²	—	5	2	no	—
147	C₂×C₃×C₄²	—	5	2	no	—
148	C₃×#95	—	5	1	no	—
149	C₃×#95	—	5	1	no	—
150	C₃×#95	—	5	2	no	—
151	C₃×#95	—	5	2	no	—
152	C₃×#95	—	5	4	no	—
153	C₃×#95	—	5	4	no	—
154	C₃×#95	—	5	4	no	—
155	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
156	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
157	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
158	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
159	Q₈×D₅	—	2	4	no	—
160	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
162	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
163	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
165	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
167	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
168	C₄⋊AGL(1,𝔽₅)	—	4	4	no	—
169	C₄×AGL(1,𝔽₅)	—	2	4	no	—
170	C₄×AGL(1,𝔽₅)	—	4	2	no	—
171	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
172	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
173	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
174	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
175	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
176	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
177	#683	C₂×C₃×C₄	1	2	yes	—
178	#683	C₂×C₃×C₄	1	2	yes	—
179	#683	C₂×C₃×C₄	1	2	yes	—
180	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
181	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
182	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
183	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
184	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
185	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂×C₄×Q₈	—	5	1	no	—
187	#391	—	5	2	no	—
188	#389	—	5	2	no	—
189	#387	—	5	4	no	—
190	#383	—	5	2	no	—
191	#382	—	5	2	no	—
192	C₄×C₄⋊C₄	—	5	1	no	—
193	#376	—	5	1	no	—
194	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₃×D₅	C₂×#41	1	2	yes	—
196	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₃×D₅	2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×C₃×D₅	2₋¹⁺⁴	1	2	yes	—
199	C₃×AGL(1,𝔽₅)	—	4	2	no	—
200	C₃×AGL(1,𝔽₅)	—	4	2	no	—
201	C₃×AGL(1,𝔽₅)	—	4	4	no	—
202	C₃×C₄×C₅	—	2	2	no	—
203	C₃×C₄×C₅	—	2	1	no	—
204	C₃×C₄×C₅	—	2	1	no	—
205	C₃×C₄×C₅	—	2	2	no	—
206	C₃×C₄×C₅	#117	1	2	yes	—
207	C₃×Dic₅	—	2	2	no	—
208	C₃×Dic₅	—	2	1	no	—
209	C₃×Dic₅	—	2	1	no	—
210	C₃×Dic₅	—	2	2	no	—
211	C₃×Dic₅	#117	1	2	yes	—
212	C₂×C₃×Q₈	—	5	2	no	—
213	C₂×C₃×Q₈	—	5	1	no	—
214	C₂×C₃×Q₈	—	10	4	no	—
215	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
216	C₂²×C₃×C₄	—	5	1	no	—
217	C₂²×C₃×C₄	—	5	1	no	—
218	C₂²×C₃×C₄	—	5	2	no	—
219	C₂²×C₃×C₄	—	5	1	no	—
220	C₂²×C₃×C₄	—	5	2	no	—
221	C₂²×C₃×C₄	—	5	2	no	—
222	C₂²×C₃×C₄	—	5	2	no	—
223	C₂²×C₃×C₄	—	5	4	no	—
224	C₃×C₄⋊C₄	—	5	2	no	—
225	C₃×C₄⋊C₄	—	5	2	no	—
226	C₃×C₄⋊C₄	—	5	2	no	—
227	C₃×C₄⋊C₄	—	5	2	no	—
228	C₃×C₄⋊C₄	—	5	1	no	—
229	C₃×C₄⋊C₄	—	10	4	no	—
230	C₃×C₄⋊C₄	—	20	4	no	—
231	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
232	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
233	C₃×C₄²	—	5	1	no	—
234	C₃×C₄²	—	5	1	no	—
235	C₃×C₄²	—	5	2	no	—
236	C₃×C₄²	—	5	1	no	—
237	C₃×C₄²	—	5	2	no	—
238	C₃×C₄²	—	5	2	no	—
239	C₃×C₄²	—	10	4	no	—
240	C₃×C₄²	—	20	2	no	—
241	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
242	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
243	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
244	C₂×AGL(1,𝔽₅)	—	2	2	no	—
245	C₂×AGL(1,𝔽₅)	—	2	2	no	—
246	C₂×AGL(1,𝔽₅)	—	2	4	no	—
247	C₂×AGL(1,𝔽₅)	—	2	4	no	—
248	C₂×AGL(1,𝔽₅)	—	2	2	no	—
249	C₂×AGL(1,𝔽₅)	—	2	2	no	—
250	C₂×AGL(1,𝔽₅)	—	2	2	no	—
251	C₂×AGL(1,𝔽₅)	—	2	2	no	—
252	C₂×AGL(1,𝔽₅)	—	2	4	no	—
253	C₅×Q₈	—	2	2	no	—
254	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
257	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
258	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
259	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
260	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
263	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₄×D₅	—	2	4	no	—
265	C₄×D₅	—	2	1	no	—
266	C₄×D₅	—	2	2	no	—
267	C₄×D₅	—	2	2	no	—
268	C₄×D₅	—	2	1	no	—
269	C₄×D₅	—	2	2	no	—
270	C₄×D₅	C₃×#41	1	4	yes	—
271	Dic₁₀	—	2	2	no	—
272	Dic₁₀	—	2	4	no	—
273	C₂²×Q₈	—	5	1	no	—
274	C₄×Q₈	—	5	1	no	—
275	C₄×Q₈	—	5	2	no	—
276	C₄×Q₈	—	5	1	no	—
277	C₄×Q₈	—	5	2	no	—
278	C₄×Q₈	—	5	1	no	—
279	C₄×Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
280	C₂×C₄⋊C₄	—	5	2	no	—
281	C₂×C₄⋊C₄	—	5	1	no	—
282	C₂×C₄⋊C₄	—	5	2	no	—
283	C₂×C₄⋊C₄	—	5	4	no	—
284	C₂×C₄²	—	5	1	no	—
285	C₂×C₄²	—	5	2	no	—
286	C₂×C₄²	—	5	2	no	—
287	C₂×C₄²	—	5	2	no	—
288	#95	—	5	1	no	—
289	#95	—	5	1	no	—
290	#95	—	5	2	no	—
291	#95	—	5	2	no	—
292	#95	—	5	4	no	—
293	#95	—	5	4	no	—
294	#95	—	5	4	no	—
295	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
296	C₂×C₃×C₅	#519	1	1	yes	characteristic
297	C₂×C₃×C₅	#520	1	1	yes	characteristic
298	C₃×D₅	#541	1	2	yes	—
299	C₃×D₅	#542	1	2	yes	—
300	C₂³×C₃	—	5	1	no	—
301	C₃×Q₈	—	2	2	no	—
302	C₃×Q₈	—	10	4	no	—
303	C₃×Q₈	—	10	2	no	—
304	C₂×C₃×C₄	—	5	1	no	—
305	C₂×C₃×C₄	—	5	4	no	—
306	C₂×C₃×C₄	—	5	1	no	—
307	C₂×C₃×C₄	—	5	1	no	—
308	C₂×C₃×C₄	—	5	2	no	—
309	C₂×C₃×C₄	—	5	2	no	—
310	C₂×C₃×C₄	—	10	1	no	—
311	C₂×C₃×C₄	—	10	2	no	—
312	C₂×C₃×C₄	—	10	2	no	—
313	C₂×C₃×C₄	—	10	1	no	—
314	C₂×C₃×C₄	—	10	2	no	—
315	C₂×C₃×C₄	—	10	4	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	4	no	—
319	C₂×C₃×C₄	—	10	4	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	10	2	no	—
322	C₂×C₃×C₄	—	10	2	no	—
323	C₂×C₃×C₄	—	10	4	no	—
324	C₂×C₃×C₄	—	10	2	no	—
325	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
328	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
329	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
330	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
331	C₂×D₅	C₂×C₃×#41	1	2	yes	—
332	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×D₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
334	C₂×D₅	C₃×2₋¹⁺⁴	1	2	yes	—
335	AGL(1,𝔽₅)	—	4	2	no	—
336	AGL(1,𝔽₅)	—	4	2	no	—
337	AGL(1,𝔽₅)	—	4	4	no	—
338	C₄×C₅	—	2	2	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	C₃×#117	1	2	yes	—
343	Dic₅	—	2	2	no	—
344	Dic₅	—	2	1	no	—
345	Dic₅	—	2	1	no	—
346	Dic₅	—	2	2	no	—
347	Dic₅	C₃×#117	1	2	yes	—
348	C₂×Q₈	—	5	2	no	—
349	C₂×Q₈	—	5	1	no	—
350	C₂×Q₈	—	10	4	no	—
351	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
352	C₂²×C₄	—	5	1	no	—
353	C₂²×C₄	—	5	1	no	—
354	C₂²×C₄	—	5	2	no	—
355	C₂²×C₄	—	5	1	no	—
356	C₂²×C₄	—	5	2	no	—
357	C₂²×C₄	—	5	2	no	—
358	C₂²×C₄	—	5	2	no	—
359	C₂²×C₄	—	5	4	no	—
360	C₄⋊C₄	—	5	2	no	—
361	C₄⋊C₄	—	5	2	no	—
362	C₄⋊C₄	—	5	2	no	—
363	C₄⋊C₄	—	5	2	no	—
364	C₄⋊C₄	—	5	1	no	—
365	C₄⋊C₄	—	10	4	no	—
366	C₄⋊C₄	—	20	4	no	—
367	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
368	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₄²	—	5	1	no	—
370	C₄²	—	5	1	no	—
371	C₄²	—	5	2	no	—
372	C₄²	—	5	1	no	—
373	C₄²	—	5	2	no	—
374	C₄²	—	5	2	no	—
375	C₄²	—	10	4	no	—
376	C₄²	—	20	2	no	—
377	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
378	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₃×C₅	#2320	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	5	2	no	—
381	C₂²×C₃	—	5	2	no	—
382	C₂²×C₃	—	5	1	no	—
383	C₂²×C₃	—	5	1	no	—
384	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	5	2	no	—
390	C₃×C₄	—	10	2	no	—
391	C₃×C₄	—	10	1	no	—
392	C₃×C₄	—	10	1	no	—
393	C₃×C₄	—	10	2	no	—
394	C₃×C₄	—	20	2	no	—
395	C₃×C₄	—	20	4	no	—
396	C₃×C₄	—	20	2	no	—
397	C₃×C₄	#4130	1	2	yes	—
398	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
399	C₂×C₅	C₃×#519	1	1	yes	characteristic
400	C₂×C₅	C₃×#520	1	1	yes	characteristic
401	D₅	C₃×#541	1	2	yes	—
402	D₅	C₃×#542	1	2	yes	—
403	C₂³	—	5	1	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	10	4	no	—
406	Q₈	—	10	2	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	4	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	1	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	5	2	no	—
413	C₂×C₄	—	10	1	no	—
414	C₂×C₄	—	10	2	no	—
415	C₂×C₄	—	10	4	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	1	no	—
418	C₂×C₄	—	10	2	no	—
419	C₂×C₄	—	10	2	no	—
420	C₂×C₄	—	10	2	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	2	no	—
426	C₂×C₄	—	10	4	no	—
427	C₂×C₄	—	10	2	no	—
428	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
431	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
432	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
433	C₂×C₃	—	5	2	no	—
434	C₂×C₃	—	5	2	no	—
435	C₂×C₃	C₂×#4130	1	1	yes	characteristic
436	C₂×C₃	#66262	1	1	yes	characteristic
437	C₂×C₃	#66266	1	1	yes	characteristic
438	C₅	C₃×#2320	1	1	yes	characteristic, complemented, Sylow
439	C₂²	—	5	2	no	—
440	C₂²	—	5	2	no	—
441	C₂²	—	5	1	no	—
442	C₂²	—	5	1	no	—
443	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	2	no	—
448	C₄	—	5	2	no	—
449	C₄	—	10	2	no	—
450	C₄	—	10	1	no	—
451	C₄	—	10	1	no	—
452	C₄	—	10	2	no	—
453	C₄	—	20	2	no	—
454	C₄	—	20	4	no	—
455	C₄	—	20	2	no	—
456	C₄	C₃×#4130	1	2	yes	—
457	C₃	#10617210	1	1	yes	characteristic, direct product factor, Sylow
458	C₂	—	5	2	no	—
459	C₂	—	5	2	no	—
460	C₂	C₂×C₃×#4130	1	1	yes	characteristic
461	C₂	C₃×#66262	1	1	yes	characteristic
462	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×C₄×C₅×Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂⁴
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×C₄×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2320
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. #10617210	C₃	direct (N × H)
15. C₃×C₄×C₅×Q₈	C₄	semidirect
16. C₃×Q₈×Dic₅	C₄	semidirect
19. C₃×#4033	C₄	semidirect
20. C₃×#4033	C₄	semidirect
23. C₃×C₄×Dic₁₀	C₄	semidirect
24. C₃×C₄×Dic₁₀	C₄	semidirect
85. C₄×C₅×Q₈	C₃×C₄	semidirect
86. Q₈×Dic₅	C₃×C₄	semidirect
89. #4033	C₃×C₄	semidirect
90. #4033	C₃×C₄	semidirect
93. C₄×Dic₁₀	C₃×C₄	semidirect
94. C₄×Dic₁₀	C₃×C₄	semidirect
139. C₃×C₄×Q₈	AGL(1,𝔽₅)	semidirect
279. C₄×Q₈	C₃×AGL(1,𝔽₅)	semidirect
379. C₃×C₅	#2320	semidirect
438. C₅	C₃×#2320	semidirect
457. C₃	#10617210	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×C₄×Q₈×D₅	2
C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	2
C₃×#65712	2
C₃×#65711	2
C₃×#65690	2
C₃×#65689	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×#65686	2
#10617210	3
C₃×#2320	5

Subgroups — C3×#10617210 #14323261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617210 #14323261