Subgroups — C₃×AGL(1,𝔽₅)×#117 #14319500

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 452 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×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	4	yes	maximal, complemented
5	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	C₂	1	4	yes	maximal
6	C₃×#65686	C₂	1	2	yes	maximal, complemented
7	C₃×C₄²×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	AGL(1,𝔽₅)×#117	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	C₄	1	8	yes	complemented
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	1	8	yes	complemented
15	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	8	yes	—
16	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	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×C₄×#117	—	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	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	4	yes	complemented
34	C₂²⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	4	yes	—
35	#65686	C₂×C₃	1	2	yes	complemented
36	C₄²×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
37	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×AGL(1,𝔽₅)	—	2	8	no	—
39	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	8	yes	—
40	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
41	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
42	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	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	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₄×D₅	C₂×C₄	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)	C₂×C₄	1	8	yes	—
53	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	8	yes	complemented
54	C₃×C₄×AGL(1,𝔽₅)	—	2	16	no	—
55	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
56	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	8	yes	—
57	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
58	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	8	yes	complemented
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×C₄²	—	5	1	no	—
71	C₃×C₄×C₄⋊C₄	—	5	4	no	—
72	C₃×C₄×C₂²⋊C₄	—	5	4	no	—
73	C₃×#376	—	5	2	no	—
74	C₃×C₄³	—	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	C₃×C₄	1	8	yes	complemented
79	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
80	C₂×C₄×AGL(1,𝔽₅)	C₃×C₄	1	8	yes	complemented
81	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	—
82	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	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	C₄×#117	—	5	1	no	Sylow
96	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	4	no	—
98	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
102	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
103	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
104	C₂×C₃×AGL(1,𝔽₅)	—	2	16	no	—
105	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	4	yes	—
106	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	—
107	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	4	yes	—
108	C₂×C₃×AGL(1,𝔽₅)	#41	1	8	yes	—
109	C₂×C₃×C₄×C₅	C₄²	1	4	yes	complemented
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×Dic₅	C₄²	1	4	yes	complemented
114	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
117	C₃×C₄×D₅	—	2	8	no	—
118	C₃×C₄×D₅	C₄²	1	4	yes	complemented
119	C₃×C₄×D₅	C₄²	1	4	yes	complemented
120	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
121	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
122	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
123	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
124	C₂³×C₃×C₄	—	5	1	no	—
125	C₂³×C₃×C₄	—	5	2	no	—
126	C₃×#117	—	5	8	no	—
127	C₃×#117	—	5	1	no	—
128	C₃×#117	—	5	2	no	—
129	C₃×#117	—	5	2	no	—
130	C₃×#117	—	5	2	no	—
131	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
132	C₂×C₃×C₄⋊C₄	—	5	2	no	—
133	C₂×C₃×C₄⋊C₄	—	5	2	no	—
134	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
135	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
136	C₂×C₃×C₄²	—	5	8	no	—
137	C₂×C₃×C₄²	—	5	1	no	—
138	C₂×C₃×C₄²	—	5	2	no	—
139	C₂×C₃×C₄²	—	5	1	no	—
140	C₂×C₃×C₄²	—	5	2	no	—
141	C₂×C₃×C₄²	—	5	2	no	—
142	C₂×C₃×C₄²	—	5	8	no	—
143	C₃×#95	—	5	8	no	—
144	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
146	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	—
147	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
148	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
149	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
150	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
155	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
156	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
157	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
159	C₂²⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	—
160	C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	complemented
161	C₄×AGL(1,𝔽₅)	—	2	16	no	—
162	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
163	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	—
164	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
165	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	8	yes	complemented
166	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	complemented
167	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
168	C₄²×C₅	C₂×C₃×C₄	1	2	yes	complemented
169	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
170	#685	C₂×C₃×C₄	1	4	yes	—
171	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	complemented
172	#683	C₂×C₃×C₄	1	4	yes	complemented
173	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
174	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	complemented
175	C₂×#117	—	5	1	no	—
176	C₂×#117	—	5	1	no	—
177	C₂²×C₄²	—	5	1	no	—
178	C₄×C₄⋊C₄	—	5	4	no	—
179	C₄×C₂²⋊C₄	—	5	4	no	—
180	#376	—	5	2	no	—
181	C₄³	—	5	2	no	—
182	C₂²×C₃×C₅	—	2	2	no	—
183	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
184	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₃×D₅	—	2	2	no	—
186	C₂×C₃×D₅	—	2	4	no	—
187	C₂×C₃×D₅	—	2	4	no	—
188	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
189	C₂×C₃×D₅	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₃×D₅	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₃×D₅	C₂×#41	1	4	yes	—
192	C₃×AGL(1,𝔽₅)	—	2	4	no	—
193	C₃×AGL(1,𝔽₅)	—	2	8	no	—
194	C₃×AGL(1,𝔽₅)	#117	1	8	yes	direct product factor
195	C₃×C₄×C₅	—	2	4	no	—
196	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
197	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
198	C₃×Dic₅	—	2	4	no	—
199	C₃×Dic₅	C₂×C₄²	1	2	yes	—
200	C₃×Dic₅	C₂×C₄²	1	2	yes	—
201	C₂⁴×C₃	—	5	1	no	—
202	C₂²×C₃×C₄	—	5	2	no	—
203	C₂²×C₃×C₄	—	5	1	no	—
204	C₂²×C₃×C₄	—	5	4	no	—
205	C₂²×C₃×C₄	—	5	4	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	1	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	—	5	1	no	—
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	—	5	4	no	—
212	C₂²×C₃×C₄	—	5	8	no	—
213	C₂²×C₃×C₄	—	5	4	no	—
214	C₂²×C₃×C₄	—	10	8	no	—
215	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
216	C₃×C₄⋊C₄	—	5	8	no	—
217	C₃×C₄⋊C₄	—	5	4	no	—
218	C₃×C₄⋊C₄	—	5	2	no	—
219	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
220	C₃×C₂²⋊C₄	—	5	8	no	—
221	C₃×C₂²⋊C₄	—	5	2	no	—
222	C₃×C₂²⋊C₄	—	5	4	no	—
223	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
224	C₃×C₄²	—	5	4	no	—
225	C₃×C₄²	—	5	8	no	—
226	C₃×C₄²	—	5	4	no	—
227	C₃×C₄²	—	5	8	no	—
228	C₃×C₄²	—	5	4	no	—
229	C₃×C₄²	—	5	2	no	—
230	C₃×C₄²	—	10	16	no	—
231	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
232	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
233	C₂²×D₅	—	2	4	no	—
234	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
235	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
236	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
237	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
238	C₂×AGL(1,𝔽₅)	—	2	8	no	—
239	C₂×AGL(1,𝔽₅)	—	2	4	no	—
240	C₂×AGL(1,𝔽₅)	—	2	16	no	—
241	C₂×AGL(1,𝔽₅)	C₂²×C₃×C₄	1	4	yes	—
242	C₂×AGL(1,𝔽₅)	C₂²×C₃×C₄	1	8	yes	—
243	C₂×AGL(1,𝔽₅)	C₂²×C₃×C₄	1	4	yes	—
244	C₂×AGL(1,𝔽₅)	C₃×#41	1	8	yes	—
245	C₂×C₄×C₅	C₃×C₄²	1	4	yes	complemented
246	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
247	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
249	C₂×Dic₅	C₃×C₄²	1	4	yes	complemented
250	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
251	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
253	C₄×D₅	—	2	8	no	—
254	C₄×D₅	C₃×C₄²	1	4	yes	complemented
255	C₄×D₅	C₃×C₄²	1	4	yes	complemented
256	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
257	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
258	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
259	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
260	C₂³×C₄	—	5	1	no	—
261	C₂³×C₄	—	5	2	no	—
262	#117	—	5	8	no	—
263	#117	—	5	1	no	—
264	#117	—	5	2	no	—
265	#117	—	5	2	no	—
266	#117	—	5	2	no	—
267	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
268	C₂×C₄⋊C₄	—	5	2	no	—
269	C₂×C₄⋊C₄	—	5	2	no	—
270	C₂×C₂²⋊C₄	—	5	2	no	—
271	C₂×C₂²⋊C₄	—	5	2	no	—
272	C₂×C₄²	—	5	2	no	—
273	C₂×C₄²	—	5	8	no	—
274	C₂×C₄²	—	5	1	no	—
275	C₂×C₄²	—	5	1	no	—
276	C₂×C₄²	—	5	2	no	—
277	C₂×C₄²	—	5	2	no	—
278	C₂×C₄²	—	5	8	no	—
279	#95	—	5	8	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
282	C₂×C₃×C₅	C₄×#41	1	2	yes	—
283	C₃×D₅	—	2	2	no	—
284	C₃×D₅	C₂×#117	1	2	yes	—
285	C₃×D₅	C₄×#41	1	2	yes	—
286	C₂³×C₃	—	5	1	no	—
287	C₂³×C₃	—	5	2	no	—
288	C₂³×C₃	—	5	2	no	—
289	C₂³×C₃	—	5	1	no	—
290	C₂³×C₃	—	10	4	no	—
291	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
292	C₂×C₃×C₄	—	5	4	no	—
293	C₂×C₃×C₄	—	5	8	no	—
294	C₂×C₃×C₄	—	5	4	no	—
295	C₂×C₃×C₄	—	5	1	no	—
296	C₂×C₃×C₄	—	5	1	no	—
297	C₂×C₃×C₄	—	5	4	no	—
298	C₂×C₃×C₄	—	5	4	no	—
299	C₂×C₃×C₄	—	5	2	no	—
300	C₂×C₃×C₄	—	5	2	no	—
301	C₂×C₃×C₄	—	5	2	no	—
302	C₂×C₃×C₄	—	5	2	no	—
303	C₂×C₃×C₄	—	5	4	no	—
304	C₂×C₃×C₄	—	5	8	no	—
305	C₂×C₃×C₄	—	5	4	no	—
306	C₂×C₃×C₄	—	10	8	no	—
307	C₂×C₃×C₄	—	10	16	no	—
308	C₂×C₃×C₄	—	10	8	no	—
309	C₂×C₃×C₄	—	10	4	no	—
310	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	4	yes	complemented
311	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	4	yes	—
312	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
316	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
317	C₂×D₅	—	2	2	no	—
318	C₂×D₅	—	2	4	no	—
319	C₂×D₅	—	2	4	no	—
320	C₂×D₅	C₂×C₃×C₄²	1	2	yes	—
321	C₂×D₅	C₂³×C₃×C₄	1	1	yes	characteristic
322	C₂×D₅	C₂³×C₃×C₄	1	1	yes	characteristic
323	C₂×D₅	C₂×C₃×#41	1	4	yes	—
324	AGL(1,𝔽₅)	—	2	4	no	—
325	AGL(1,𝔽₅)	—	2	8	no	—
326	AGL(1,𝔽₅)	C₃×#117	1	8	yes	direct product factor
327	C₄×C₅	—	2	4	no	—
328	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
329	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
330	Dic₅	—	2	4	no	—
331	Dic₅	C₂×C₃×C₄²	1	2	yes	—
332	Dic₅	C₂×C₃×C₄²	1	2	yes	—
333	C₂⁴	—	5	1	no	—
334	C₂²×C₄	—	5	2	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	—	5	4	no	—
337	C₂²×C₄	—	5	4	no	—
338	C₂²×C₄	—	5	1	no	—
339	C₂²×C₄	—	5	1	no	—
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	2	no	—
343	C₂²×C₄	—	5	4	no	—
344	C₂²×C₄	—	5	8	no	—
345	C₂²×C₄	—	5	4	no	—
346	C₂²×C₄	—	10	8	no	—
347	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
348	C₄⋊C₄	—	5	8	no	—
349	C₄⋊C₄	—	5	4	no	—
350	C₄⋊C₄	—	5	2	no	—
351	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
352	C₂²⋊C₄	—	5	8	no	—
353	C₂²⋊C₄	—	5	2	no	—
354	C₂²⋊C₄	—	5	4	no	—
355	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
356	C₄²	—	5	4	no	—
357	C₄²	—	5	8	no	—
358	C₄²	—	5	4	no	—
359	C₄²	—	5	8	no	—
360	C₄²	—	5	4	no	—
361	C₄²	—	5	2	no	—
362	C₄²	—	10	16	no	—
363	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
364	C₃×C₅	C₄×#117	1	1	yes	characteristic, complemented, Hall
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	5	1	no	—
367	C₂²×C₃	—	5	1	no	—
368	C₂²×C₃	—	5	4	no	—
369	C₂²×C₃	—	5	2	no	—
370	C₂²×C₃	—	10	4	no	—
371	C₂²×C₃	—	10	4	no	—
372	C₂²×C₃	—	10	2	no	—
373	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
374	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	5	8	no	—
377	C₃×C₄	—	5	2	no	—
378	C₃×C₄	—	5	2	no	—
379	C₃×C₄	—	10	8	no	—
380	C₃×C₄	—	10	4	no	—
381	C₃×C₄	—	10	4	no	—
382	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
383	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
384	C₂×C₅	—	2	2	no	—
385	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
386	C₂×C₅	C₃×C₄×#41	1	2	yes	—
387	D₅	—	2	2	no	—
388	D₅	C₂×C₃×#117	1	2	yes	—
389	D₅	C₃×C₄×#41	1	2	yes	—
390	C₂³	—	5	1	no	—
391	C₂³	—	5	2	no	—
392	C₂³	—	5	2	no	—
393	C₂³	—	5	1	no	—
394	C₂³	—	10	4	no	—
395	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
396	C₂×C₄	—	5	4	no	—
397	C₂×C₄	—	5	8	no	—
398	C₂×C₄	—	5	4	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	5	2	no	—
402	C₂×C₄	—	5	2	no	—
403	C₂×C₄	—	5	2	no	—
404	C₂×C₄	—	5	2	no	—
405	C₂×C₄	—	5	4	no	—
406	C₂×C₄	—	5	4	no	—
407	C₂×C₄	—	5	4	no	—
408	C₂×C₄	—	5	8	no	—
409	C₂×C₄	—	5	4	no	—
410	C₂×C₄	—	10	8	no	—
411	C₂×C₄	—	10	16	no	—
412	C₂×C₄	—	10	8	no	—
413	C₂×C₄	—	10	4	no	—
414	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	4	yes	complemented
415	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
416	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	—	5	2	no	—
420	C₂×C₃	—	5	2	no	—
421	C₂×C₃	—	10	2	no	—
422	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
423	C₂×C₃	#41×AGL(1,𝔽₅)	1	2	yes	—
424	C₅	C₃×C₄×#117	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	2	no	—
426	C₂²	—	5	1	no	—
427	C₂²	—	5	1	no	—
428	C₂²	—	5	4	no	—
429	C₂²	—	5	2	no	—
430	C₂²	—	10	4	no	—
431	C₂²	—	10	4	no	—
432	C₂²	—	10	2	no	—
433	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
434	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	5	8	no	—
437	C₄	—	5	2	no	—
438	C₄	—	5	2	no	—
439	C₄	—	10	4	no	—
440	C₄	—	10	8	no	—
441	C₄	—	10	4	no	—
442	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
443	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
444	C₃	AGL(1,𝔽₅)×#117	1	1	yes	characteristic, direct product factor, Sylow
445	C₂	—	2	2	no	—
446	C₂	—	5	2	no	—
447	C₂	—	5	2	no	—
448	C₂	—	10	2	no	—
449	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
450	C₂	C₃×#41×AGL(1,𝔽₅)	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
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×C₄×#117
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

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
6. C₃×#65686	C₂	semidirect
7. C₃×C₄²×AGL(1,𝔽₅)	C₂	semidirect
8. AGL(1,𝔽₅)×#117	C₃	direct (N × H)
12. C₃×#4130	C₄	semidirect
14. C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	semidirect
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. C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	semidirect
35. #65686	C₂×C₃	semidirect
36. C₄²×AGL(1,𝔽₅)	C₂×C₃	semidirect
53. C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	semidirect
58. C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	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
78. #4130	C₃×C₄	semidirect
80. C₂×C₄×AGL(1,𝔽₅)	C₃×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
109. C₂×C₃×C₄×C₅	C₄²	semidirect
113. C₂×C₃×Dic₅	C₄²	semidirect
118. C₃×C₄×D₅	C₄²	semidirect
119. C₃×C₄×D₅	C₄²	semidirect
131. C₃×#117	AGL(1,𝔽₅)	direct (N × H)
160. C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	semidirect
165. C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	semidirect
166. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
168. C₄²×C₅	C₂×C₃×C₄	semidirect
171. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
172. #683	C₂×C₃×C₄	semidirect
173. C₄×Dic₅	C₂×C₃×C₄	semidirect
174. C₄×Dic₅	C₂×C₃×C₄	semidirect
194. C₃×AGL(1,𝔽₅)	#117	direct (N × H)
219. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
231. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
245. C₂×C₄×C₅	C₃×C₄²	semidirect
249. C₂×Dic₅	C₃×C₄²	semidirect
254. C₄×D₅	C₃×C₄²	semidirect
255. C₄×D₅	C₃×C₄²	semidirect
267. #117	C₃×AGL(1,𝔽₅)	direct (N × H)
310. C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	semidirect
326. AGL(1,𝔽₅)	C₃×#117	direct (N × H)
351. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
363. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
364. C₃×C₅	C₄×#117	semidirect
414. C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	semidirect
424. C₅	C₃×C₄×#117	semidirect
444. C₃	AGL(1,𝔽₅)×#117	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×C₄⋊C₄×AGL(1,𝔽₅)	2
C₃×C₂²⋊C₄×AGL(1,𝔽₅)	2
C₃×#65686	2
C₃×C₄²×AGL(1,𝔽₅)	2
AGL(1,𝔽₅)×#117	3
C₃×C₄×#117	5

Subgroups — C3×AGL(1,𝔽5)×#117 #14319500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×AGL(1,𝔽₅)×#117 #14319500