Subgroups — C₃×C₄×#4130 #14319498

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 416 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	2	yes	maximal
2	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₂²⋊AGL(1,𝔽₅)	C₂	1	4	yes	maximal
4	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	4	yes	maximal, complemented
5	C₃×#65686	C₂	1	2	yes	maximal, complemented
6	C₃×C₄²×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
7	C₄×#4130	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
11	C₃×#4130	C₄	1	16	yes	direct product factor
12	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
13	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	8	yes	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	4	yes	—
15	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic, complemented
16	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×C₄×Dic₅	C₄	1	2	yes	complemented
18	C₃×C₄²×D₅	C₄	1	2	yes	complemented
19	C₃×C₄²×D₅	C₄	1	1	yes	characteristic, complemented
20	C₃×C₄²×D₅	C₄	1	1	yes	characteristic, complemented
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
23	C₃×C₄²×D₅	C₂²	1	2	yes	—
24	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	8	yes	—
25	C₃×C₄×#117	—	5	1	no	maximal, Hall
26	C₂×#4130	C₂×C₃	1	2	yes	—
27	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
28	C₄×C₂²⋊AGL(1,𝔽₅)	C₂×C₃	1	4	yes	—
29	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	4	yes	complemented
30	#65686	C₂×C₃	1	2	yes	complemented
31	C₄²×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
32	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
33	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	8	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	—	2	8	no	—
39	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
44	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
45	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
48	C₃×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	16	yes	—
49	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	16	yes	complemented
50	C₃×C₄×AGL(1,𝔽₅)	—	2	16	no	—
51	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	16	yes	complemented
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
57	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
58	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
59	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
60	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
61	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×#117	—	5	2	no	—
63	C₂²×C₃×C₄²	—	5	1	no	—
64	C₃×C₄×C₄⋊C₄	—	5	4	no	—
65	C₃×C₄×C₂²⋊C₄	—	5	4	no	—
66	C₃×#376	—	5	2	no	—
67	C₃×C₄³	—	5	2	no	—
68	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
69	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
71	#4130	C₃×C₄	1	16	yes	direct product factor
72	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
73	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	—
74	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
75	C₂×C₄²×C₅	C₃×C₄	1	1	yes	characteristic, complemented
76	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₅	C₃×C₄	1	2	yes	complemented
78	C₄²×D₅	C₃×C₄	1	2	yes	complemented
79	C₄²×D₅	C₃×C₄	1	1	yes	characteristic, complemented
80	C₄²×D₅	C₃×C₄	1	1	yes	characteristic, complemented
81	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
82	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
83	C₄²×D₅	C₂²×C₃	1	2	yes	—
84	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	8	yes	—
85	C₄×#117	—	5	1	no	Sylow
86	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₃×D₅	—	2	4	no	—
88	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
90	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
91	C₂×C₃×AGL(1,𝔽₅)	—	2	16	no	—
92	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	16	yes	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	C₄²	1	4	yes	complemented
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×Dic₅	—	2	4	no	—
100	C₂×C₃×Dic₅	C₄²	1	4	yes	complemented
101	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
105	C₃×C₄×D₅	—	2	4	no	—
106	C₃×C₄×D₅	—	2	4	no	—
107	C₃×C₄×D₅	—	2	4	no	—
108	C₃×C₄×D₅	C₄²	1	4	yes	complemented
109	C₃×C₄×D₅	C₄²	1	4	yes	complemented
110	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
111	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
112	C₃×C₄×D₅	#41	1	8	yes	—
113	C₂³×C₃×C₄	—	5	1	no	—
114	C₂³×C₃×C₄	—	5	2	no	—
115	C₃×#117	—	5	16	no	—
116	C₂×C₃×C₄⋊C₄	—	5	4	no	—
117	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
118	C₂×C₃×C₄²	—	5	4	no	—
119	C₂×C₃×C₄²	—	5	2	no	—
120	C₂×C₃×C₄²	—	5	1	no	—
121	C₂×C₃×C₄²	—	5	1	no	—
122	C₂×C₃×C₄²	—	5	2	no	—
123	C₂×C₃×C₄²	—	5	1	no	—
124	C₂×C₃×C₄²	—	5	2	no	—
125	C₂×C₃×C₄²	—	5	1	no	—
126	C₂×C₃×C₄²	—	5	1	no	—
127	C₂×C₃×C₄²	—	5	8	no	—
128	C₂×C₃×C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
129	C₃×#95	—	5	8	no	—
130	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
131	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	8	yes	—
132	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
133	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
135	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₄×D₅	—	2	8	no	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
139	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
141	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
142	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
143	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
145	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
146	C₂²⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	16	yes	—
147	C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	16	yes	complemented
148	C₄×AGL(1,𝔽₅)	—	2	16	no	—
149	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	16	yes	complemented
150	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
151	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
152	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
154	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
155	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
156	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
157	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
158	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
159	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
160	C₂×#117	—	5	2	no	—
161	C₂²×C₄²	—	5	1	no	—
162	C₄×C₄⋊C₄	—	5	4	no	—
163	C₄×C₂²⋊C₄	—	5	4	no	—
164	#376	—	5	2	no	—
165	C₄³	—	5	2	no	—
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
168	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₃×D₅	—	2	2	no	—
170	C₂×C₃×D₅	—	2	8	no	—
171	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
172	C₂×C₃×D₅	C₂³×C₄	1	2	yes	—
173	C₂×C₃×D₅	C₂×#41	1	4	yes	—
174	C₃×AGL(1,𝔽₅)	—	2	16	no	—
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
177	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
178	C₃×C₄×C₅	#117	1	4	yes	complemented
179	C₃×Dic₅	—	2	2	no	—
180	C₃×Dic₅	C₂×C₄²	1	2	yes	—
181	C₃×Dic₅	C₂×C₄²	1	2	yes	—
182	C₃×Dic₅	#117	1	4	yes	complemented
183	C₂⁴×C₃	—	5	1	no	—
184	C₂²×C₃×C₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	8	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	1	no	—
188	C₂²×C₃×C₄	—	5	1	no	—
189	C₂²×C₃×C₄	—	5	2	no	—
190	C₂²×C₃×C₄	—	5	1	no	—
191	C₂²×C₃×C₄	—	5	8	no	—
192	C₂²×C₃×C₄	—	5	2	no	—
193	C₂²×C₃×C₄	—	5	2	no	—
194	C₂²×C₃×C₄	—	5	2	no	—
195	C₂²×C₃×C₄	—	5	2	no	—
196	C₂²×C₃×C₄	—	10	8	no	—
197	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
198	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
199	C₃×C₄⋊C₄	—	5	16	no	—
200	C₃×C₂²⋊C₄	—	5	16	no	—
201	C₃×C₄²	—	5	16	no	—
202	C₃×C₄²	—	5	2	no	—
203	C₃×C₄²	—	5	1	no	—
204	C₃×C₄²	—	5	2	no	—
205	C₃×C₄²	—	5	2	no	—
206	C₃×C₄²	—	5	2	no	—
207	C₃×C₄²	—	5	2	no	—
208	C₃×C₄²	—	5	1	no	—
209	C₃×C₄²	—	10	16	no	—
210	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
211	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
212	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
213	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
214	C₂²×D₅	—	2	4	no	—
215	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
216	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
217	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
218	C₂×AGL(1,𝔽₅)	—	2	16	no	—
219	C₂×AGL(1,𝔽₅)	C₂²×C₃×C₄	1	16	yes	—
220	C₂×C₄×C₅	—	2	4	no	—
221	C₂×C₄×C₅	C₃×C₄²	1	4	yes	complemented
222	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
223	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
226	C₂×Dic₅	—	2	4	no	—
227	C₂×Dic₅	C₃×C₄²	1	4	yes	complemented
228	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
229	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
232	C₄×D₅	—	2	4	no	—
233	C₄×D₅	—	2	4	no	—
234	C₄×D₅	—	2	4	no	—
235	C₄×D₅	C₃×C₄²	1	4	yes	complemented
236	C₄×D₅	C₃×C₄²	1	4	yes	complemented
237	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
238	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
239	C₄×D₅	C₃×#41	1	8	yes	—
240	C₂³×C₄	—	5	1	no	—
241	C₂³×C₄	—	5	2	no	—
242	#117	—	5	16	no	—
243	C₂×C₄⋊C₄	—	5	4	no	—
244	C₂×C₂²⋊C₄	—	5	4	no	—
245	C₂×C₄²	—	5	4	no	—
246	C₂×C₄²	—	5	2	no	—
247	C₂×C₄²	—	5	1	no	—
248	C₂×C₄²	—	5	1	no	—
249	C₂×C₄²	—	5	1	no	—
250	C₂×C₄²	—	5	2	no	—
251	C₂×C₄²	—	5	1	no	—
252	C₂×C₄²	—	5	2	no	—
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	—	5	8	no	—
255	C₂×C₄²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
256	#95	—	5	8	no	—
257	C₂×C₃×C₅	—	2	2	no	—
258	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
259	C₂×C₃×C₅	C₂×#117	1	2	yes	—
260	C₃×D₅	—	2	2	no	—
261	C₃×D₅	C₄×#41	1	4	yes	—
262	C₂³×C₃	—	5	1	no	—
263	C₂³×C₃	—	5	4	no	—
264	C₂³×C₃	—	5	1	no	—
265	C₂³×C₃	—	10	4	no	—
266	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	5	4	no	—
269	C₂×C₃×C₄	—	5	1	no	—
270	C₂×C₃×C₄	—	5	1	no	—
271	C₂×C₃×C₄	—	5	2	no	—
272	C₂×C₃×C₄	—	5	4	no	—
273	C₂×C₃×C₄	—	5	4	no	—
274	C₂×C₃×C₄	—	5	4	no	—
275	C₂×C₃×C₄	—	5	4	no	—
276	C₂×C₃×C₄	—	5	8	no	—
277	C₂×C₃×C₄	—	5	16	no	—
278	C₂×C₃×C₄	—	5	2	no	—
279	C₂×C₃×C₄	—	10	4	no	—
280	C₂×C₃×C₄	—	10	4	no	—
281	C₂×C₃×C₄	—	10	4	no	—
282	C₂×C₃×C₄	—	10	16	no	—
283	C₂×C₃×C₄	—	10	4	no	—
284	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	4	yes	complemented
285	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
286	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
291	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
292	C₂×D₅	—	2	2	no	—
293	C₂×D₅	—	2	8	no	—
294	C₂×D₅	C₂×C₃×C₄²	1	2	yes	—
295	C₂×D₅	C₂³×C₃×C₄	1	2	yes	—
296	C₂×D₅	C₂×C₃×#41	1	4	yes	—
297	AGL(1,𝔽₅)	—	2	16	no	—
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
300	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
301	C₄×C₅	C₃×#117	1	4	yes	complemented
302	Dic₅	—	2	2	no	—
303	Dic₅	C₂×C₃×C₄²	1	2	yes	—
304	Dic₅	C₂×C₃×C₄²	1	2	yes	—
305	Dic₅	C₃×#117	1	4	yes	complemented
306	C₂⁴	—	5	1	no	—
307	C₂²×C₄	—	5	1	no	—
308	C₂²×C₄	—	5	8	no	—
309	C₂²×C₄	—	5	1	no	—
310	C₂²×C₄	—	5	2	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	8	no	—
315	C₂²×C₄	—	5	2	no	—
316	C₂²×C₄	—	5	2	no	—
317	C₂²×C₄	—	5	2	no	—
318	C₂²×C₄	—	5	2	no	—
319	C₂²×C₄	—	10	8	no	—
320	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
321	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₄⋊C₄	—	5	16	no	—
323	C₂²⋊C₄	—	5	16	no	—
324	C₄²	—	5	16	no	—
325	C₄²	—	5	2	no	—
326	C₄²	—	5	1	no	—
327	C₄²	—	5	2	no	—
328	C₄²	—	5	2	no	—
329	C₄²	—	5	2	no	—
330	C₄²	—	5	2	no	—
331	C₄²	—	5	1	no	—
332	C₄²	—	10	16	no	—
333	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
334	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
335	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₃×C₅	C₄×#117	1	1	yes	characteristic, complemented, Hall
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	5	2	no	—
339	C₂²×C₃	—	5	4	no	—
340	C₂²×C₃	—	5	2	no	—
341	C₂²×C₃	—	10	8	no	—
342	C₂²×C₃	—	10	2	no	—
343	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
344	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	5	2	no	—
347	C₃×C₄	—	5	2	no	—
348	C₃×C₄	—	5	4	no	—
349	C₃×C₄	—	10	16	no	—
350	C₃×C₄	—	10	2	no	—
351	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
352	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
353	C₃×C₄	#4130	1	4	yes	direct product factor
354	C₂×C₅	—	2	2	no	—
355	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
356	C₂×C₅	C₂×C₃×#117	1	2	yes	—
357	D₅	—	2	2	no	—
358	D₅	C₃×C₄×#41	1	4	yes	—
359	C₂³	—	5	1	no	—
360	C₂³	—	5	4	no	—
361	C₂³	—	5	1	no	—
362	C₂³	—	10	4	no	—
363	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	5	4	no	—
366	C₂×C₄	—	5	1	no	—
367	C₂×C₄	—	5	1	no	—
368	C₂×C₄	—	5	2	no	—
369	C₂×C₄	—	5	4	no	—
370	C₂×C₄	—	5	4	no	—
371	C₂×C₄	—	5	4	no	—
372	C₂×C₄	—	5	4	no	—
373	C₂×C₄	—	5	8	no	—
374	C₂×C₄	—	5	16	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	10	4	no	—
377	C₂×C₄	—	10	4	no	—
378	C₂×C₄	—	10	4	no	—
379	C₂×C₄	—	10	16	no	—
380	C₂×C₄	—	10	4	no	—
381	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	4	yes	complemented
382	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
383	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
386	C₂×C₃	—	2	2	no	—
387	C₂×C₃	—	5	4	no	—
388	C₂×C₃	—	10	2	no	—
389	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₂×C₃	C₂×#4130	1	2	yes	—
391	C₅	C₃×C₄×#117	1	1	yes	characteristic, complemented, Sylow
392	C₂²	—	2	2	no	—
393	C₂²	—	5	2	no	—
394	C₂²	—	5	4	no	—
395	C₂²	—	5	2	no	—
396	C₂²	—	10	8	no	—
397	C₂²	—	10	2	no	—
398	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
399	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	5	2	no	—
402	C₄	—	5	2	no	—
403	C₄	—	5	4	no	—
404	C₄	—	10	16	no	—
405	C₄	—	10	2	no	—
406	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
407	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
408	C₄	C₃×#4130	1	4	yes	direct product factor
409	C₃	C₄×#4130	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	5	4	no	—
412	C₂	—	10	2	no	—
413	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
414	C₂	C₂×C₃×#4130	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄²×C₅	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄²	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₄×#117
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
5. C₃×#65686	C₂	semidirect
6. C₃×C₄²×AGL(1,𝔽₅)	C₂	semidirect
7. C₄×#4130	C₃	direct (N × H)
11. C₃×#4130	C₄	direct (N × H)
15. C₂×C₃×C₄²×C₅	C₄	semidirect
16. C₂×C₃×C₄×Dic₅	C₄	semidirect
17. C₂×C₃×C₄×Dic₅	C₄	semidirect
18. C₃×C₄²×D₅	C₄	semidirect
19. C₃×C₄²×D₅	C₄	semidirect
20. C₃×C₄²×D₅	C₄	semidirect
29. C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
30. #65686	C₂×C₃	semidirect
31. C₄²×AGL(1,𝔽₅)	C₂×C₃	semidirect
49. C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	semidirect
51. C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	semidirect
71. #4130	C₃×C₄	direct (N × H)
75. C₂×C₄²×C₅	C₃×C₄	semidirect
76. C₂×C₄×Dic₅	C₃×C₄	semidirect
77. C₂×C₄×Dic₅	C₃×C₄	semidirect
78. C₄²×D₅	C₃×C₄	semidirect
79. C₄²×D₅	C₃×C₄	semidirect
80. C₄²×D₅	C₃×C₄	semidirect
94. C₂×C₃×C₄×C₅	C₄²	semidirect
100. C₂×C₃×Dic₅	C₄²	semidirect
108. C₃×C₄×D₅	C₄²	semidirect
109. C₃×C₄×D₅	C₄²	semidirect
128. C₂×C₃×C₄²	AGL(1,𝔽₅)	semidirect
147. C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	semidirect
149. C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	semidirect
178. C₃×C₄×C₅	#117	semidirect
182. C₃×Dic₅	#117	semidirect
221. C₂×C₄×C₅	C₃×C₄²	semidirect
227. C₂×Dic₅	C₃×C₄²	semidirect
235. C₄×D₅	C₃×C₄²	semidirect
236. C₄×D₅	C₃×C₄²	semidirect
255. C₂×C₄²	C₃×AGL(1,𝔽₅)	semidirect
284. C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	semidirect
301. C₄×C₅	C₃×#117	semidirect
305. Dic₅	C₃×#117	semidirect
336. C₃×C₅	C₄×#117	semidirect
353. C₃×C₄	#4130	direct (N × H)
381. C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	semidirect
391. C₅	C₃×C₄×#117	semidirect
408. C₄	C₃×#4130	direct (N × H)
409. C₃	C₄×#4130	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
C₂×C₃×C₄²×D₅	2
C₃×C₄×C₂²⋊AGL(1,𝔽₅)	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×#65686	2
C₃×C₄²×AGL(1,𝔽₅)	2
C₄×#4130	3
C₃×C₄×#117	5

Subgroups — C3×C4×#4130 #14319498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4130 #14319498