Subgroups — AGL(1,𝔽₅)×#11713200 #72244458

Order 15360.

At least 24172 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

The subgroup lattice has 235 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,𝔽₅)×#72991	C₂	1	1	yes	maximal, characteristic, complemented
2	AGL(1,𝔽₅)×#1020⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#72243964	C₂	1	1	yes	maximal, characteristic, complemented
4	#72243922	C₂	1	1	yes	maximal, characteristic, complemented
5	#72243722	C₂	1	1	yes	maximal, characteristic, complemented
6	#72243698	C₂	1	1	yes	maximal, characteristic, complemented
7	AGL(1,𝔽₅)×#73081	C₂	1	1	yes	maximal, characteristic, complemented
8	#72243541	C₂	1	1	yes	maximal, characteristic, complemented
9	#72243514	C₂	1	1	yes	maximal, characteristic, complemented
10	#72243472	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#11713200	C₂	1	1	yes	maximal, characteristic
12	#72243416	C₄	1	1	yes	characteristic, complemented
13	#72243415	C₄	1	1	yes	characteristic, complemented
14	#72243405	C₄	1	1	yes	characteristic, complemented
15	#72243403	C₄	1	1	yes	characteristic, complemented
16	#72243382	C₄	1	1	yes	characteristic, complemented
17	#72243374	C₄	1	1	yes	characteristic, complemented
18	#72243340	C₄	1	1	yes	characteristic, complemented
19	C₅×#11713200	C₄	1	1	yes	characteristic, complemented
20	C₂×AGL(1,𝔽₅)×#1020⋊C₂	C₂	1	1	yes	maximal, characteristic, complemented
21	AGL(1,𝔽₅)×AΣL(1,𝔽₆₄)	C₂	1	1	yes	maximal, characteristic, complemented
22	#72243178	C₂²	1	1	yes	characteristic, complemented
23	#72243171	C₂²	1	1	yes	characteristic, complemented
24	D₅×#72991	C₂²	1	1	yes	characteristic
25	#72243158	C₂²	1	1	yes	characteristic, complemented
26	D₅×#1020⋊C₄	C₂²	1	1	yes	characteristic
27	AGL(1,𝔽₅)×#379⋊C₃	C₂²	1	1	yes	characteristic, complemented
28	#72243142	C₂²	1	1	yes	characteristic, complemented
29	#72243137	C₂²	1	1	yes	characteristic, complemented
30	#72243137	C₂²	1	1	yes	characteristic, complemented
31	#72243137	C₂²	1	1	yes	characteristic, complemented
32	C₂×#1020⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
33	C₂×#1020⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
34	C₂×#1020⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic, complemented
35	#72243123	C₂²	1	1	yes	characteristic, complemented
36	#72243115	C₂²	1	1	yes	characteristic, complemented
37	C₂²×AGL(1,𝔽₅)×#1020	C₂	1	1	yes	maximal, characteristic, complemented
38	#72243076	C₂²	1	1	yes	characteristic, complemented
39	D₅×#73081	C₂²	1	1	yes	characteristic
40	C₂×#14512453	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₅×#1020⋊C₂	C₂²	1	1	yes	characteristic
42	#72243059	C₂²	1	1	yes	characteristic, complemented
43	D₅×AΣL(1,𝔽₆₄)	C₂²	1	1	yes	characteristic
44	C₂×AGL(1,𝔽₅)×#120⋊C₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#11757174	C₂²	1	1	yes	characteristic, complemented
46	C₂²×D₅×#1020	C₂²	1	1	yes	characteristic
47	AGL(1,𝔽₅)×#87524	C₂	1	1	yes	maximal, characteristic, complemented
48	#72242754	C₂²	1	1	yes	characteristic, complemented
49	C₂²×AGL(1,𝔽₅)×C₂²⋊A₄	C₂²	1	1	yes	characteristic, complemented
50	D₅×#87524	C₂²	1	1	yes	characteristic
51	#72242735	C₂²	1	1	yes	characteristic, complemented
52	#72242734	C₂²	1	1	yes	characteristic, complemented
53	AGL(1,𝔽₅)×#5936	C₂²	1	1	yes	characteristic, complemented
54	AGL(1,𝔽₅)×#2846	D₃	1	1	yes	characteristic, complemented
55	C₂×AGL(1,𝔽₅)×#1020	C₂²	1	1	yes	characteristic
56	C₂×AGL(1,𝔽₅)×#1020	C₂²	1	1	yes	characteristic
57	C₂×AGL(1,𝔽₅)×#1020	C₂²	1	1	yes	characteristic, complemented
58	C₂×AGL(1,𝔽₅)×#1020	C₂²	1	1	yes	characteristic, complemented
59	C₂×AGL(1,𝔽₅)×#1020	C₂²	1	1	yes	characteristic, complemented
60	C₂²×D₅×C₂²⋊A₄	C₂³	1	1	yes	characteristic
61	C₂²×C₅⋊#1020	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×D₅×#1020	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂×D₅×#1020	C₂×C₄	1	1	yes	characteristic, complemented
64	C₂×D₅×#1020	C₂³	1	1	yes	characteristic
65	C₂×D₅×#1020	C₂³	1	1	yes	characteristic
66	C₂×D₅×#1020	C₂³	1	1	yes	characteristic
67	C₂×AGL(1,𝔽₅)×C₂²⋊A₄	C₂³	1	1	yes	characteristic
68	C₂×AGL(1,𝔽₅)×C₂²⋊A₄	C₂³	1	1	yes	characteristic
69	C₂×#11757174	C₂³	1	1	yes	characteristic
70	C₂×#11757174	C₂³	1	1	yes	characteristic
71	C₂×#11757174	C₂³	1	1	yes	characteristic
72	C₂×#11757174	C₂³	1	1	yes	characteristic
73	AGL(1,𝔽₅)×#1020	D₄	1	4	yes	complemented
74	#14514642	C₂×C₄	1	1	yes	characteristic, complemented
75	#14514566	C₂×C₄	1	1	yes	characteristic, complemented
76	#14514565	C₂×C₄	1	1	yes	characteristic, complemented
77	D₅×#5936	C₂³	1	1	yes	characteristic
78	C₂×D₅×#120⋊C₃	C₂³	1	1	yes	characteristic
79	C₂×#11752115	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂×#1020⋊D₅	C₂×C₄	1	1	yes	characteristic, complemented
81	C₂×#1020⋊D₅	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂×#65800⋊C₃	C₂³	1	1	yes	characteristic
83	C₂×#65800⋊C₃	C₂³	1	1	yes	characteristic
84	#10615859⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented
85	#10614343⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented
86	#10605592⋊C₃	C₂×C₄	1	1	yes	characteristic, complemented
87	D₅×#379⋊C₃	C₂³	1	1	yes	characteristic
88	#14511995	C₂×C₄	1	1	yes	characteristic, complemented
89	#14511905	C₂×C₄	1	1	yes	characteristic, complemented
90	#14511904	C₂×C₄	1	1	yes	characteristic, complemented
91	#14511893	C₂×C₄	1	1	yes	characteristic, complemented
92	#14511892	C₂×C₄	1	1	yes	characteristic, complemented
93	#14511890	C₂×C₄	1	1	yes	characteristic, complemented
94	#14511890	C₂×C₄	1	1	yes	characteristic, complemented
95	#14511889	C₂×C₄	1	1	yes	characteristic, complemented
96	#1020⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
97	C₂²×C₅×#1020	C₂×C₄	1	1	yes	characteristic, complemented
98	C₅×#87524	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂×C₅×#1020⋊C₂	C₂×C₄	1	1	yes	characteristic, complemented
100	C₅×AΣL(1,𝔽₆₄)	C₂×C₄	1	1	yes	characteristic, complemented
101	C₅×#73081	C₂×C₄	1	1	yes	characteristic, complemented
102	C₅×#72991	C₂×C₄	1	1	yes	characteristic, complemented
103	C₅×#1020⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
104	C₂⁶×AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic, complemented
105	C₂×AGL(1,𝔽₅)×#120	C₂×D₃	1	1	yes	characteristic, complemented
106	#13028921	C₂×D₃	1	1	yes	characteristic, complemented
107	#13028920	C₂×D₃	1	1	yes	characteristic, complemented
108	#13028906	C₂×D₃	1	1	yes	characteristic, complemented
109	AGL(1,𝔽₅)×#379	C₂×D₃	1	1	yes	characteristic, complemented
110	D₅×#2846	C₂×D₃	1	1	yes	characteristic
111	C₂²×C₅×C₂²⋊A₄	C₂²×C₄	1	1	yes	characteristic, complemented
112	C₂×D₅×C₂²⋊A₄	C₂²×C₄	1	1	yes	characteristic, complemented
113	C₂×D₅×C₂²⋊A₄	C₂⁴	1	1	yes	characteristic
114	C₂×C₅⋊#1020	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₅⋊#1020	C₂²×C₄	1	1	yes	characteristic, complemented
116	C₂×C₅⋊#1020	C₂²×C₄	1	1	yes	characteristic, complemented
117	C₂×C₅×#1020	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×#1020	C₂²×C₄	1	1	yes	characteristic, complemented
119	C₂×C₅×#1020	C₂²×C₄	1	1	yes	characteristic, complemented
120	D₅×#1020	C₂×D₄	1	2	yes	—
121	D₅×#1020	#41	1	2	yes	—
122	AGL(1,𝔽₅)×C₂²⋊A₄	C₂×D₄	1	2	yes	complemented
123	#11757174	C₂×D₄	1	2	yes	complemented
124	#11756927	C₂²×C₄	1	1	yes	characteristic, complemented
125	C₅×#5936	C₂²×C₄	1	1	yes	characteristic, complemented
126	C₂×C₅×#120⋊C₃	C₂²×C₄	1	1	yes	characteristic, complemented
127	C₂×C₅⋊(#120⋊C₃)	C₂²×C₄	1	1	yes	characteristic, complemented
128	C₅×#379⋊C₃	C₂²×C₄	1	1	yes	characteristic, complemented
129	#65536⋊C₃	C₂²×C₄	1	1	yes	characteristic, complemented
130	#11713200	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
131	C₂⁶×D₅	C₂²×D₃	1	1	yes	characteristic
132	C₂⁵×AGL(1,𝔽₅)	C₂²×D₃	1	1	yes	characteristic
133	C₂⁵×AGL(1,𝔽₅)	C₂²×D₃	1	1	yes	characteristic
134	C₂²×D₄×AGL(1,𝔽₅)	S₄	1	1	yes	characteristic, complemented
135	C₂×D₅×#120	C₂²×D₃	1	1	yes	characteristic
136	C₂×#65800	C₂²×D₃	1	1	yes	characteristic
137	C₂×#65800	C₂²×D₃	1	1	yes	characteristic
138	C₅×#2846	C₄×D₃	1	1	yes	characteristic, complemented
139	#10615859	C₄×D₃	1	1	yes	characteristic, complemented
140	#10614343	C₄×D₃	1	1	yes	characteristic, complemented
141	#10605592	C₄×D₃	1	1	yes	characteristic, complemented
142	D₅×#379	C₂²×D₃	1	1	yes	characteristic
143	C₂×C₅×C₂²⋊A₄	C₂³×C₄	1	1	yes	characteristic
144	D₅×C₂²⋊A₄	C₂²×D₄	1	1	yes	characteristic
145	D₅×C₂²⋊A₄	C₂×#41	1	1	yes	characteristic
146	C₅⋊#1020	C₄×D₄	1	2	yes	complemented
147	C₅×#1020	C₄×D₄	1	2	yes	complemented
148	C₂²×#1020	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
149	#87524	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
150	C₂×#1020⋊C₂	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
151	AΣL(1,𝔽₆₄)	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
152	#73081	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
153	#72991	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
154	#1020⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
155	C₂⁶×C₅	C₂×C₄×D₃	1	1	yes	characteristic, complemented
156	C₂⁵×D₅	C₂×C₄×D₃	1	1	yes	characteristic, complemented
157	C₂⁵×D₅	C₂³×D₃	1	1	yes	characteristic
158	C₂⁴×AGL(1,𝔽₅)	D₃×D₄	1	2	yes	complemented
159	C₂⁴×AGL(1,𝔽₅)	C₂×S₄	1	1	yes	characteristic
160	C₂⁴×AGL(1,𝔽₅)	C₂×S₄	1	1	yes	characteristic, complemented
161	C₂²×D₄×D₅	C₂×S₄	1	1	yes	characteristic
162	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×S₄	1	1	yes	characteristic
163	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×S₄	1	1	yes	characteristic, complemented
164	C₂²×C₄⋊AGL(1,𝔽₅)	C₂×S₄	1	1	yes	characteristic, complemented
165	C₂²×C₄×AGL(1,𝔽₅)	C₂×S₄	1	1	yes	characteristic, complemented
166	C₂×C₅×#120	C₂×C₄×D₃	1	1	yes	characteristic, complemented
167	C₂×#4099	C₂×C₄×D₃	1	1	yes	characteristic, complemented
168	C₅×#379	C₂×C₄×D₃	1	1	yes	characteristic, complemented
169	#65536	C₂×C₄×D₃	1	1	yes	characteristic, complemented
170	C₅×C₂²⋊A₄	C₂×C₄×D₄	1	1	yes	characteristic, complemented
171	C₂²×C₂²⋊A₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
172	C₂×#1020	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
173	C₂×#1020	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
174	C₂×#1020	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
175	#5936	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
176	C₂×#120⋊C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
177	#379⋊C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
178	C₂⁵×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
179	C₂⁴×D₅	C₂×D₃×D₄	1	1	yes	characteristic
180	C₂⁴×D₅	D₃×#41	1	1	yes	characteristic
181	C₂⁴×D₅	C₂²×S₄	1	1	yes	characteristic
182	C₂⁴×D₅	C₂²×S₄	1	1	yes	characteristic
183	C₂³×AGL(1,𝔽₅)	C₂²×S₄	1	1	yes	characteristic
184	C₂³×AGL(1,𝔽₅)	C₂²×S₄	1	1	yes	characteristic
185	C₂³×AGL(1,𝔽₅)	C₂²×S₄	1	1	yes	characteristic
186	C₂³×AGL(1,𝔽₅)	C₂²×S₄	1	1	yes	characteristic
187	C₂²×C₅×D₄	C₄×S₄	1	1	yes	characteristic, complemented
188	C₂²×C₂²⋊D₅	C₄×S₄	1	1	yes	characteristic, complemented
189	C₂²×C₂²⋊D₅	C₄×S₄	1	1	yes	characteristic, complemented
190	C₂²×D₂₀	C₄×S₄	1	1	yes	characteristic, complemented
191	C₂²×C₄×D₅	C₂²×S₄	1	1	yes	characteristic
192	#2846	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
193	C₂×C₂²⋊A₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
194	#1020	D₄×AGL(1,𝔽₅)	1	2	yes	complemented
195	C₂⁴×C₅	C₄×D₃×D₄	1	1	yes	characteristic, complemented
196	C₂⁴×C₅	C₂×C₄×S₄	1	1	yes	characteristic
197	C₂⁴×C₅	C₂×C₄×S₄	1	1	yes	characteristic, complemented
198	C₂³×D₅	C₂×C₄×S₄	1	1	yes	characteristic
199	C₂³×D₅	C₂×C₄×S₄	1	1	yes	characteristic, complemented
200	C₂³×D₅	C₂³×S₄	1	1	yes	characteristic
201	C₂²×AGL(1,𝔽₅)	#1020⋊C₂	1	1	yes	characteristic, complemented
202	C₂²×AGL(1,𝔽₅)	D₄×S₄	1	2	yes	—
203	C₂²×C₄×C₅	C₂×C₄×S₄	1	1	yes	characteristic, complemented
204	C₂²×Dic₅	C₂×C₄×S₄	1	1	yes	characteristic, complemented
205	C₂⁶	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
206	C₂×#120	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
207	#379	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
208	C₂²⋊A₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
209	C₂³×C₅	C₂²×C₄×S₄	1	1	yes	characteristic
210	C₂²×D₅	C₂×#1020⋊C₂	1	1	yes	characteristic
211	C₂²×D₅	C₂×D₄×S₄	1	1	yes	characteristic
212	C₂²×D₅	#41×S₄	1	1	yes	characteristic
213	C₂×AGL(1,𝔽₅)	C₂×#1020⋊C₂	1	1	yes	characteristic
214	C₂×AGL(1,𝔽₅)	C₂×#1020⋊C₂	1	1	yes	characteristic
215	C₂⁵	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
216	C₂²×D₄	AGL(1,𝔽₅)×S₄	1	1	yes	characteristic, complemented
217	C₂²×C₅	C₄×#1020⋊C₂	1	1	yes	characteristic, complemented
218	C₂²×C₅	C₄×D₄×S₄	1	1	yes	characteristic
219	C₂×D₅	C₄×#1020⋊C₂	1	1	yes	characteristic, complemented
220	C₂×D₅	C₂²×#1020⋊C₂	1	1	yes	characteristic
221	AGL(1,𝔽₅)	#11713200	1	2	yes	direct product factor
222	C₂⁴	D₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
223	C₂⁴	C₂×AGL(1,𝔽₅)×S₄	1	1	yes	characteristic
224	C₂⁴	C₂×AGL(1,𝔽₅)×S₄	1	1	yes	characteristic, complemented
225	C₂²×C₄	C₂×AGL(1,𝔽₅)×S₄	1	1	yes	characteristic, complemented
226	C₂×C₅	C₂×C₄×#1020⋊C₂	1	1	yes	characteristic
227	D₅	C₂×#11713200	1	1	yes	characteristic
228	D₅	#72220637	1	1	yes	characteristic
229	C₂³	C₂²×AGL(1,𝔽₅)×S₄	1	1	yes	characteristic
230	C₅	C₄×#11713200	1	1	yes	characteristic, complemented, Sylow
231	C₂²	AGL(1,𝔽₅)×#1020⋊C₂	1	1	yes	characteristic, complemented
232	C₂²	D₄×AGL(1,𝔽₅)×S₄	1	1	yes	characteristic
233	C₂	C₂×AGL(1,𝔽₅)×#1020⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×AGL(1,𝔽₅)×#1020⋊C₂
commutator	C₂×C₅×C₂²⋊A₄	C₂³×C₄
Frattini	C₂³	C₂²×AGL(1,𝔽₅)×S₄
Fitting	C₅×#2846	C₄×D₃
socle	C₂³×C₅	C₂²×C₄×S₄
prime radical	D₅×#11713200	C₂
cosocle	C₂×D₅×C₂²⋊A₄	C₂⁴
hypercenter	C₂²	AGL(1,𝔽₅)×#1020⋊C₂
hypocenter	C₅×C₂²⋊A₄	C₂×C₄×D₄
LCS	G ▷ C₂×C₅×C₂²⋊A₄ ▷ C₅×C₂²⋊A₄
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. AGL(1,𝔽₅)×#72991	C₂	semidirect
2. AGL(1,𝔽₅)×#1020⋊C₄	C₂	semidirect
3. #72243964	C₂	semidirect
4. #72243922	C₂	semidirect
5. #72243722	C₂	semidirect
6. #72243698	C₂	semidirect
7. AGL(1,𝔽₅)×#73081	C₂	semidirect
8. #72243541	C₂	semidirect
9. #72243514	C₂	semidirect
10. #72243472	C₂	semidirect
12. #72243416	C₄	semidirect
13. #72243415	C₄	semidirect
14. #72243405	C₄	semidirect
15. #72243403	C₄	semidirect
16. #72243382	C₄	semidirect
17. #72243374	C₄	semidirect
18. #72243340	C₄	semidirect
19. C₅×#11713200	C₄	semidirect
20. C₂×AGL(1,𝔽₅)×#1020⋊C₂	C₂	semidirect
21. AGL(1,𝔽₅)×AΣL(1,𝔽₆₄)	C₂	semidirect
22. #72243178	C₂²	semidirect
23. #72243171	C₂²	semidirect
25. #72243158	C₂²	semidirect
27. AGL(1,𝔽₅)×#379⋊C₃	C₂²	semidirect
28. #72243142	C₂²	semidirect
29. #72243137	C₂²	semidirect
30. #72243137	C₂²	semidirect
31. #72243137	C₂²	semidirect
34. C₂×#1020⋊AGL(1,𝔽₅)	C₂²	semidirect
35. #72243123	C₂²	semidirect
36. #72243115	C₂²	semidirect
37. C₂²×AGL(1,𝔽₅)×#1020	C₂	semidirect
38. #72243076	C₂²	semidirect
40. C₂×#14512453	C₂²	semidirect
42. #72243059	C₂²	semidirect
44. C₂×AGL(1,𝔽₅)×#120⋊C₃	C₂²	semidirect
45. C₂²×#11757174	C₂²	semidirect
47. AGL(1,𝔽₅)×#87524	C₂	semidirect
48. #72242754	C₂²	semidirect
49. C₂²×AGL(1,𝔽₅)×C₂²⋊A₄	C₂²	semidirect
51. #72242735	C₂²	semidirect
52. #72242734	C₂²	semidirect
53. AGL(1,𝔽₅)×#5936	C₂²	semidirect
54. AGL(1,𝔽₅)×#2846	D₃	semidirect
57. C₂×AGL(1,𝔽₅)×#1020	C₂²	semidirect
58. C₂×AGL(1,𝔽₅)×#1020	C₂²	semidirect
59. C₂×AGL(1,𝔽₅)×#1020	C₂²	semidirect
61. C₂²×C₅⋊#1020	C₂×C₄	semidirect
62. C₂×D₅×#1020	C₂×C₄	semidirect
63. C₂×D₅×#1020	C₂×C₄	semidirect
73. AGL(1,𝔽₅)×#1020	D₄	semidirect
74. #14514642	C₂×C₄	semidirect
75. #14514566	C₂×C₄	semidirect
76. #14514565	C₂×C₄	semidirect
79. C₂×#11752115	C₂×C₄	semidirect
80. C₂×#1020⋊D₅	C₂×C₄	semidirect
81. C₂×#1020⋊D₅	C₂×C₄	semidirect
84. #10615859⋊C₃	C₂×C₄	semidirect
85. #10614343⋊C₃	C₂×C₄	semidirect
86. #10605592⋊C₃	C₂×C₄	semidirect
88. #14511995	C₂×C₄	semidirect
89. #14511905	C₂×C₄	semidirect
90. #14511904	C₂×C₄	semidirect
91. #14511893	C₂×C₄	semidirect
92. #14511892	C₂×C₄	semidirect
93. #14511890	C₂×C₄	semidirect
94. #14511890	C₂×C₄	semidirect
95. #14511889	C₂×C₄	semidirect
96. #1020⋊Dic₅	C₂×C₄	semidirect
97. C₂²×C₅×#1020	C₂×C₄	semidirect
98. C₅×#87524	C₂×C₄	semidirect
99. C₂×C₅×#1020⋊C₂	C₂×C₄	semidirect
100. C₅×AΣL(1,𝔽₆₄)	C₂×C₄	semidirect
101. C₅×#73081	C₂×C₄	semidirect
102. C₅×#72991	C₂×C₄	semidirect
103. C₅×#1020⋊C₄	C₂×C₄	semidirect
104. C₂⁶×AGL(1,𝔽₅)	C₂×D₃	semidirect
105. C₂×AGL(1,𝔽₅)×#120	C₂×D₃	semidirect
106. #13028921	C₂×D₃	semidirect
107. #13028920	C₂×D₃	semidirect
108. #13028906	C₂×D₃	semidirect
109. AGL(1,𝔽₅)×#379	C₂×D₃	semidirect
111. C₂²×C₅×C₂²⋊A₄	C₂²×C₄	semidirect
112. C₂×D₅×C₂²⋊A₄	C₂²×C₄	semidirect
115. C₂×C₅⋊#1020	C₂²×C₄	semidirect
116. C₂×C₅⋊#1020	C₂²×C₄	semidirect
118. C₂×C₅×#1020	C₂²×C₄	semidirect
119. C₂×C₅×#1020	C₂²×C₄	semidirect
122. AGL(1,𝔽₅)×C₂²⋊A₄	C₂×D₄	semidirect
123. #11757174	C₂×D₄	semidirect
124. #11756927	C₂²×C₄	semidirect
125. C₅×#5936	C₂²×C₄	semidirect
126. C₂×C₅×#120⋊C₃	C₂²×C₄	semidirect
127. C₂×C₅⋊(#120⋊C₃)	C₂²×C₄	semidirect
128. C₅×#379⋊C₃	C₂²×C₄	semidirect
129. #65536⋊C₃	C₂²×C₄	semidirect
130. #11713200	AGL(1,𝔽₅)	direct (N × H)
134. C₂²×D₄×AGL(1,𝔽₅)	S₄	semidirect
138. C₅×#2846	C₄×D₃	semidirect
139. #10615859	C₄×D₃	semidirect
140. #10614343	C₄×D₃	semidirect
141. #10605592	C₄×D₃	semidirect
146. C₅⋊#1020	C₄×D₄	semidirect
147. C₅×#1020	C₄×D₄	semidirect
148. C₂²×#1020	C₂×AGL(1,𝔽₅)	semidirect
149. #87524	C₂×AGL(1,𝔽₅)	semidirect
150. C₂×#1020⋊C₂	C₂×AGL(1,𝔽₅)	semidirect
151. AΣL(1,𝔽₆₄)	C₂×AGL(1,𝔽₅)	semidirect
152. #73081	C₂×AGL(1,𝔽₅)	semidirect
153. #72991	C₂×AGL(1,𝔽₅)	semidirect
154. #1020⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
155. C₂⁶×C₅	C₂×C₄×D₃	semidirect
156. C₂⁵×D₅	C₂×C₄×D₃	semidirect
158. C₂⁴×AGL(1,𝔽₅)	D₃×D₄	semidirect
160. C₂⁴×AGL(1,𝔽₅)	C₂×S₄	semidirect
163. C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×S₄	semidirect
164. C₂²×C₄⋊AGL(1,𝔽₅)	C₂×S₄	semidirect
165. C₂²×C₄×AGL(1,𝔽₅)	C₂×S₄	semidirect
166. C₂×C₅×#120	C₂×C₄×D₃	semidirect
167. C₂×#4099	C₂×C₄×D₃	semidirect
168. C₅×#379	C₂×C₄×D₃	semidirect
169. #65536	C₂×C₄×D₃	semidirect
170. C₅×C₂²⋊A₄	C₂×C₄×D₄	semidirect
171. C₂²×C₂²⋊A₄	C₂²×AGL(1,𝔽₅)	semidirect
173. C₂×#1020	C₂²×AGL(1,𝔽₅)	semidirect
174. C₂×#1020	C₂²×AGL(1,𝔽₅)	semidirect
175. #5936	C₂²×AGL(1,𝔽₅)	semidirect
176. C₂×#120⋊C₃	C₂²×AGL(1,𝔽₅)	semidirect
177. #379⋊C₃	C₂²×AGL(1,𝔽₅)	semidirect
187. C₂²×C₅×D₄	C₄×S₄	semidirect
188. C₂²×C₂²⋊D₅	C₄×S₄	semidirect
189. C₂²×C₂²⋊D₅	C₄×S₄	semidirect
190. C₂²×D₂₀	C₄×S₄	semidirect
192. #2846	D₃×AGL(1,𝔽₅)	semidirect
194. #1020	D₄×AGL(1,𝔽₅)	semidirect
195. C₂⁴×C₅	C₄×D₃×D₄	semidirect
197. C₂⁴×C₅	C₂×C₄×S₄	semidirect
199. C₂³×D₅	C₂×C₄×S₄	semidirect
201. C₂²×AGL(1,𝔽₅)	#1020⋊C₂	semidirect
203. C₂²×C₄×C₅	C₂×C₄×S₄	semidirect
204. C₂²×Dic₅	C₂×C₄×S₄	semidirect
205. C₂⁶	C₂×D₃×AGL(1,𝔽₅)	semidirect
206. C₂×#120	C₂×D₃×AGL(1,𝔽₅)	semidirect
207. #379	C₂×D₃×AGL(1,𝔽₅)	semidirect
208. C₂²⋊A₄	C₂×D₄×AGL(1,𝔽₅)	semidirect
216. C₂²×D₄	AGL(1,𝔽₅)×S₄	semidirect
217. C₂²×C₅	C₄×#1020⋊C₂	semidirect
219. C₂×D₅	C₄×#1020⋊C₂	semidirect
221. AGL(1,𝔽₅)	#11713200	direct (N × H)
222. C₂⁴	D₃×D₄×AGL(1,𝔽₅)	semidirect
224. C₂⁴	C₂×AGL(1,𝔽₅)×S₄	semidirect
225. C₂²×C₄	C₂×AGL(1,𝔽₅)×S₄	semidirect
230. C₅	C₄×#11713200	semidirect
231. C₂²	AGL(1,𝔽₅)×#1020⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₄×#11713200	5
AGL(1,𝔽₅)×#72991	2
AGL(1,𝔽₅)×#1020⋊C₄	2
#72243964	2
#72243922	2
#72243722	2
#72243698	2
AGL(1,𝔽₅)×#73081	2
#72243541	2
#72243514	2
#72243472	2
D₅×#11713200	2
C₂×AGL(1,𝔽₅)×#1020⋊C₂	2
AGL(1,𝔽₅)×AΣL(1,𝔽₆₄)	2
C₂²×AGL(1,𝔽₅)×#1020	2
AGL(1,𝔽₅)×#87524	2
AGL(1,𝔽₅)×#23900	3
D₄×AGL(1,𝔽₅)×S₄	4

Subgroups — AGL(1,𝔽5)×#11713200 #72244458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×#11713200 #72244458