Subgroups — C₂×AGL(1,𝔽₅)×AGL(1,𝔽₁₃) #72246799

Order 6240.

432 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊AGL(1,𝔽₁₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×AGL(1,𝔽₅)×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×AGL(1,𝔽₁₃)	C₂	1	1	yes	maximal, characteristic
4	C₂×AGL(1,𝔽₅)×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	AGL(1,𝔽₅)×AGL(1,𝔽₁₃)	C₂	1	4	yes	maximal, direct product factor
6	C₂×D₅×D₁₃⋊C₃	C₂²	1	1	yes	characteristic
7	C₂×#63118⋊C₃	C₄	1	1	yes	characteristic, complemented
8	C₂×#63120⋊C₃	C₄	1	1	yes	characteristic, complemented
9	C₂×#63122⋊C₃	C₄	1	1	yes	characteristic, complemented
10	C₂×#63121⋊C₃	C₄	1	1	yes	characteristic, complemented
11	C₂×AGL(1,𝔽₅)×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented
12	C₂×C₅×AGL(1,𝔽₁₃)	C₄	1	1	yes	characteristic, complemented
13	D₅×AGL(1,𝔽₁₃)	C₄	1	2	yes	complemented
14	D₅×AGL(1,𝔽₁₃)	C₂²	1	2	yes	—
15	AGL(1,𝔽₅)×D₁₃⋊C₃	C₄	1	2	yes	complemented
16	AGL(1,𝔽₅)×D₁₃⋊C₃	C₂²	1	2	yes	—
17	D₅⋊AGL(1,𝔽₁₃)	C₄	1	2	yes	complemented
18	D₅⋊AGL(1,𝔽₁₃)	C₂²	1	2	yes	—
19	C₂×C₄×AGL(1,𝔽₁₃)	—	5	1	no	maximal, Hall
20	C₂×D₅×#261	C₂×C₃	1	1	yes	characteristic
21	C₂×AGL(1,𝔽₅)×D₁₃	C₂×C₃	1	1	yes	characteristic
22	C₂×D₅⋊#261	C₂×C₃	1	1	yes	characteristic
23	AGL(1,𝔽₅)×#261	C₂×C₃	1	4	yes	complemented
24	C₂×C₅⋊(D₁₃⋊C₃)	C₂×C₄	1	1	yes	characteristic
25	C₂×D₅×C₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₅×D₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
27	D₅×D₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
28	D₅×D₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
29	D₅×D₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
30	D₅×D₁₃⋊C₃	C₂³	1	1	yes	characteristic
31	#63118⋊C₃	C₂×C₄	1	2	yes	complemented
32	#63120⋊C₃	C₂×C₄	1	2	yes	complemented
33	#63121⋊C₃	C₂×C₄	1	2	yes	complemented
34	#63122⋊C₃	C₂×C₄	1	2	yes	complemented
35	AGL(1,𝔽₅)×C₁₃⋊C₃	C₂×C₄	1	2	yes	complemented
36	C₅×AGL(1,𝔽₁₃)	C₂×C₄	1	2	yes	complemented
37	C₂²×AGL(1,𝔽₁₃)	—	5	1	no	—
38	C₂²×AGL(1,𝔽₁₃)	—	5	1	no	—
39	C₂×C₄×D₁₃⋊C₃	—	5	1	no	—
40	C₄×AGL(1,𝔽₁₃)	—	5	4	no	—
41	C₂×D₅×D₁₃	C₂²×C₃	1	1	yes	characteristic
42	C₂×#63118	C₃×C₄	1	1	yes	characteristic, complemented
43	C₂×#63120	C₃×C₄	1	1	yes	characteristic, complemented
44	C₂×#63121	C₃×C₄	1	1	yes	characteristic, complemented
45	C₂×#63122	C₃×C₄	1	1	yes	characteristic, complemented
46	C₂×C₁₃×AGL(1,𝔽₅)	C₃×C₄	1	1	yes	characteristic, complemented
47	C₂×C₅×#261	C₃×C₄	1	1	yes	characteristic, complemented
48	D₅×#261	C₃×C₄	1	2	yes	complemented
49	D₅×#261	C₂²×C₃	1	2	yes	—
50	AGL(1,𝔽₅)×D₁₃	C₃×C₄	1	2	yes	complemented
51	AGL(1,𝔽₅)×D₁₃	C₂²×C₃	1	2	yes	—
52	D₅⋊#261	C₃×C₄	1	2	yes	complemented
53	D₅⋊#261	C₂²×C₃	1	2	yes	—
54	C₂×C₃×C₄×AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
55	C₂×C₄×#261	—	5	1	no	Hall
56	C₂×C₅×C₁₃⋊C₃	C₄²	1	1	yes	characteristic, complemented
57	C₅⋊(D₁₃⋊C₃)	C₄²	1	1	yes	characteristic, complemented
58	C₅⋊(D₁₃⋊C₃)	C₂²×C₄	1	1	yes	characteristic
59	D₅×C₁₃⋊C₃	C₄²	1	1	yes	characteristic, complemented
60	D₅×C₁₃⋊C₃	C₂²×C₄	1	1	yes	characteristic
61	C₅×D₁₃⋊C₃	C₄²	1	1	yes	characteristic, complemented
62	C₅×D₁₃⋊C₃	C₂²×C₄	1	1	yes	characteristic
63	C₂²×D₁₃⋊C₃	—	5	1	no	—
64	C₂×AGL(1,𝔽₁₃)	—	5	2	no	—
65	C₂×AGL(1,𝔽₁₃)	—	5	2	no	—
66	C₂×AGL(1,𝔽₁₃)	—	5	1	no	—
67	C₂×AGL(1,𝔽₁₃)	—	5	1	no	—
68	C₂×AGL(1,𝔽₁₃)	—	5	1	no	—
69	C₂×AGL(1,𝔽₁₃)	—	5	2	no	—
70	C₂×AGL(1,𝔽₁₃)	—	5	2	no	—
71	C₂×AGL(1,𝔽₁₃)	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
72	C₂×C₄×C₁₃⋊C₃	—	5	1	no	—
73	C₂×Dic₁₃⋊C₃	—	5	1	no	—
74	C₄×D₁₃⋊C₃	—	5	2	no	—
75	C₄×D₁₃⋊C₃	—	5	2	no	—
76	C₂×D₆₅	C₂×C₃×C₄	1	1	yes	characteristic
77	C₂×D₅×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
78	C₂×C₅×D₁₃	C₂×C₃×C₄	1	1	yes	characteristic
79	D₅×D₁₃	C₂×C₃×C₄	1	1	yes	characteristic
80	D₅×D₁₃	C₂×C₃×C₄	1	1	yes	characteristic
81	D₅×D₁₃	C₂×C₃×C₄	1	1	yes	characteristic
82	D₅×D₁₃	C₂³×C₃	1	1	yes	characteristic
83	#63122	C₂×C₃×C₄	1	2	yes	complemented
84	#63121	C₂×C₃×C₄	1	2	yes	complemented
85	#63120	C₂×C₃×C₄	1	2	yes	complemented
86	C₁₃×AGL(1,𝔽₅)	C₂×C₃×C₄	1	2	yes	complemented
87	#63118	C₂×C₃×C₄	1	2	yes	complemented
88	C₅×#261	C₂×C₃×C₄	1	2	yes	complemented
89	C₂²×C₃×AGL(1,𝔽₅)	—	13	1	no	—
90	C₂²×C₃×AGL(1,𝔽₅)	—	13	1	no	—
91	C₂×C₃×C₄×D₅	—	13	1	no	—
92	C₃×C₄×AGL(1,𝔽₅)	—	13	4	no	—
93	C₂²×#261	—	5	1	no	—
94	C₂²×#261	—	5	1	no	—
95	C₂×C₄×D₁₃	—	5	1	no	—
96	C₄×#261	—	5	4	no	—
97	C₅×C₁₃⋊C₃	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
98	C₂×C₄×AGL(1,𝔽₅)	—	13	1	no	Hall
99	C₂²×C₁₃⋊C₃	—	5	1	no	—
100	C₂×D₁₃⋊C₃	—	5	1	no	—
101	C₂×D₁₃⋊C₃	—	5	1	no	—
102	C₂×D₁₃⋊C₃	—	5	1	no	—
103	C₂×D₁₃⋊C₃	—	5	1	no	—
104	C₂×D₁₃⋊C₃	—	5	1	no	—
105	C₂×D₁₃⋊C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
106	AGL(1,𝔽₁₃)	—	5	2	no	—
107	AGL(1,𝔽₁₃)	—	5	2	no	—
108	AGL(1,𝔽₁₃)	—	5	2	no	—
109	AGL(1,𝔽₁₃)	C₂×AGL(1,𝔽₅)	1	2	yes	direct product factor
110	C₄×C₁₃⋊C₃	—	5	2	no	—
111	Dic₁₃⋊C₃	—	5	2	no	—
112	C₂×C₅×C₁₃	C₃×C₄²	1	1	yes	characteristic, complemented
113	D₆₅	C₃×C₄²	1	1	yes	characteristic, complemented
114	D₆₅	C₂²×C₃×C₄	1	1	yes	characteristic
115	C₅×D₁₃	C₃×C₄²	1	1	yes	characteristic, complemented
116	C₅×D₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
117	D₅×C₁₃	C₃×C₄²	1	1	yes	characteristic, complemented
118	D₅×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
119	C₂²×C₃×D₅	—	13	1	no	—
120	C₂×C₃×AGL(1,𝔽₅)	—	13	2	no	—
121	C₂×C₃×AGL(1,𝔽₅)	—	13	2	no	—
122	C₂×C₃×AGL(1,𝔽₅)	—	13	1	no	—
123	C₂×C₃×AGL(1,𝔽₅)	—	13	1	no	—
124	C₂×C₃×AGL(1,𝔽₅)	—	13	1	no	—
125	C₂×C₃×AGL(1,𝔽₅)	—	13	2	no	—
126	C₂×C₃×AGL(1,𝔽₅)	—	13	2	no	—
127	C₂×C₃×AGL(1,𝔽₅)	—	52	1	no	—
128	C₂×C₃×C₄×C₅	—	13	1	no	—
129	C₂×C₃×Dic₅	—	13	1	no	—
130	C₃×C₄×D₅	—	13	2	no	—
131	C₃×C₄×D₅	—	13	2	no	—
132	C₂²×D₁₃	—	5	1	no	—
133	C₂×#261	—	5	2	no	—
134	C₂×#261	—	5	2	no	—
135	C₂×#261	—	5	1	no	—
136	C₂×#261	—	5	1	no	—
137	C₂×#261	—	5	1	no	—
138	C₂×#261	—	5	2	no	—
139	C₂×#261	—	5	2	no	—
140	C₂×#261	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
141	C₂×C₄×C₁₃	—	5	1	no	—
142	C₂×Dic₁₃	—	5	1	no	—
143	C₄×D₁₃	—	5	2	no	—
144	C₄×D₁₃	—	5	2	no	—
145	C₂×C₃×C₄²	—	65	1	no	Hall
146	C₂²×AGL(1,𝔽₅)	—	13	1	no	—
147	C₂²×AGL(1,𝔽₅)	—	13	1	no	—
148	C₂×C₄×D₅	—	13	1	no	—
149	C₄×AGL(1,𝔽₅)	—	13	4	no	—
150	C₂×C₁₃⋊C₃	—	5	1	no	—
151	C₂×C₁₃⋊C₃	—	5	1	no	—
152	C₂×C₁₃⋊C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
153	D₁₃⋊C₃	—	5	1	no	—
154	D₁₃⋊C₃	—	5	1	no	—
155	D₁₃⋊C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
156	D₁₃⋊C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
157	C₅×C₁₃	C₂×C₃×C₄²	1	1	yes	characteristic, complemented, Hall
158	C₂²×C₃×C₅	—	13	1	no	—
159	C₂×C₃×D₅	—	13	1	no	—
160	C₂×C₃×D₅	—	13	1	no	—
161	C₂×C₃×D₅	—	13	1	no	—
162	C₂×C₃×D₅	—	13	1	no	—
163	C₂×C₃×D₅	—	13	1	no	—
164	C₂×C₃×D₅	—	52	1	no	—
165	C₃×AGL(1,𝔽₅)	—	13	2	no	—
166	C₃×AGL(1,𝔽₅)	—	13	2	no	—
167	C₃×AGL(1,𝔽₅)	—	13	2	no	—
168	C₃×AGL(1,𝔽₅)	—	52	2	no	—
169	C₃×C₄×C₅	—	13	2	no	—
170	C₃×Dic₅	—	13	2	no	—
171	C₂²×C₁₃	—	5	1	no	—
172	C₂×D₁₃	—	5	1	no	—
173	C₂×D₁₃	—	5	1	no	—
174	C₂×D₁₃	—	5	1	no	—
175	C₂×D₁₃	—	5	1	no	—
176	C₂×D₁₃	—	5	1	no	—
177	C₂×D₁₃	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
178	#261	—	5	2	no	—
179	#261	—	5	2	no	—
180	#261	—	5	2	no	—
181	#261	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
182	C₄×C₁₃	—	5	2	no	—
183	Dic₁₃	—	5	2	no	—
184	C₂²×C₃×C₄	—	65	1	no	—
185	C₂²×C₃×C₄	—	65	1	no	—
186	C₂²×C₃×C₄	—	65	1	no	—
187	C₃×C₄²	—	65	4	no	—
188	C₂²×D₅	—	13	1	no	—
189	C₂×AGL(1,𝔽₅)	—	13	2	no	—
190	C₂×AGL(1,𝔽₅)	—	13	2	no	—
191	C₂×AGL(1,𝔽₅)	—	13	1	no	—
192	C₂×AGL(1,𝔽₅)	—	13	1	no	—
193	C₂×AGL(1,𝔽₅)	—	13	1	no	—
194	C₂×AGL(1,𝔽₅)	—	13	2	no	—
195	C₂×AGL(1,𝔽₅)	—	13	2	no	—
196	C₂×AGL(1,𝔽₅)	AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor
197	C₂×C₄×C₅	—	13	1	no	—
198	C₂×Dic₅	—	13	1	no	—
199	C₄×D₅	—	13	2	no	—
200	C₄×D₅	—	13	2	no	—
201	C₁₃⋊C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
202	C₂×C₄²	—	65	1	no	Sylow
203	C₂×C₃×C₅	—	13	1	no	—
204	C₂×C₃×C₅	—	13	1	no	—
205	C₂×C₃×C₅	—	52	1	no	—
206	C₃×D₅	—	13	1	no	—
207	C₃×D₅	—	13	1	no	—
208	C₃×D₅	—	52	1	no	—
209	C₃×D₅	—	52	1	no	—
210	C₂×C₁₃	—	5	1	no	—
211	C₂×C₁₃	—	5	1	no	—
212	C₂×C₁₃	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
213	D₁₃	—	5	1	no	—
214	D₁₃	—	5	1	no	—
215	D₁₃	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
216	D₁₃	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
217	C₂³×C₃	—	65	1	no	—
218	C₂×C₃×C₄	—	260	1	no	—
219	C₂×C₃×C₄	—	13	1	no	—
220	C₂×C₃×C₄	—	65	2	no	—
221	C₂×C₃×C₄	—	65	2	no	—
222	C₂×C₃×C₄	—	65	2	no	—
223	C₂×C₃×C₄	—	65	2	no	—
224	C₂×C₃×C₄	—	65	1	no	—
225	C₂×C₃×C₄	—	65	1	no	—
226	C₂×C₃×C₄	—	65	2	no	—
227	C₂×C₃×C₄	—	65	2	no	—
228	C₂×C₃×C₄	—	65	1	no	—
229	C₂×C₃×C₄	—	65	1	no	—
230	C₂²×C₅	—	13	1	no	—
231	C₂×D₅	—	13	1	no	—
232	C₂×D₅	—	13	1	no	—
233	C₂×D₅	—	13	1	no	—
234	C₂×D₅	—	13	1	no	—
235	C₂×D₅	—	13	1	no	—
236	C₂×D₅	C₂×AGL(1,𝔽₁₃)	1	1	yes	characteristic
237	AGL(1,𝔽₅)	—	13	2	no	—
238	AGL(1,𝔽₅)	—	13	2	no	—
239	AGL(1,𝔽₅)	—	13	2	no	—
240	AGL(1,𝔽₅)	C₂×AGL(1,𝔽₁₃)	1	2	yes	direct product factor
241	C₄×C₅	—	13	2	no	—
242	Dic₅	—	13	2	no	—
243	C₂²×C₄	—	65	1	no	—
244	C₂²×C₄	—	65	1	no	—
245	C₂²×C₄	—	65	1	no	—
246	C₄²	—	65	4	no	—
247	C₃×C₅	—	52	1	no	Hall
248	C₁₃	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
249	C₂²×C₃	—	260	1	no	—
250	C₂²×C₃	—	13	1	no	—
251	C₂²×C₃	—	65	1	no	—
252	C₂²×C₃	—	65	1	no	—
253	C₂²×C₃	—	65	1	no	—
254	C₂²×C₃	—	65	1	no	—
255	C₂²×C₃	—	65	1	no	—
256	C₃×C₄	—	260	2	no	—
257	C₃×C₄	—	13	2	no	—
258	C₃×C₄	—	65	2	no	—
259	C₃×C₄	—	65	2	no	—
260	C₃×C₄	—	65	2	no	—
261	C₃×C₄	—	65	2	no	—
262	C₂×C₅	—	13	1	no	—
263	C₂×C₅	—	13	1	no	—
264	C₂×C₅	C₄×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
265	D₅	—	13	1	no	—
266	D₅	—	13	1	no	—
267	D₅	C₄×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
268	D₅	C₂²×AGL(1,𝔽₁₃)	1	1	yes	characteristic
269	C₂³	—	65	1	no	—
270	C₂×C₄	—	5	1	no	—
271	C₂×C₄	—	13	1	no	—
272	C₂×C₄	—	65	2	no	—
273	C₂×C₄	—	65	2	no	—
274	C₂×C₄	—	65	2	no	—
275	C₂×C₄	—	65	2	no	—
276	C₂×C₄	—	65	1	no	—
277	C₂×C₄	—	65	1	no	—
278	C₂×C₄	—	65	2	no	—
279	C₂×C₄	—	65	2	no	—
280	C₂×C₄	—	65	1	no	—
281	C₂×C₄	—	65	1	no	—
282	C₂×C₃	—	260	1	no	—
283	C₂×C₃	—	260	1	no	—
284	C₂×C₃	—	13	1	no	—
285	C₂×C₃	—	13	1	no	—
286	C₂×C₃	—	52	1	no	—
287	C₂×C₃	—	65	1	no	—
288	C₂×C₃	—	65	1	no	—
289	C₅	C₂×C₄×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
290	C₂²	—	5	1	no	—
291	C₂²	—	13	1	no	—
292	C₂²	—	65	1	no	—
293	C₂²	—	65	1	no	—
294	C₂²	—	65	1	no	—
295	C₂²	—	65	1	no	—
296	C₂²	—	65	1	no	—
297	C₄	—	5	2	no	—
298	C₄	—	13	2	no	—
299	C₄	—	65	2	no	—
300	C₄	—	65	2	no	—
301	C₄	—	65	2	no	—
302	C₄	—	65	2	no	—
303	C₃	—	52	1	no	Sylow
304	C₂	—	5	1	no	—
305	C₂	—	5	1	no	—
306	C₂	—	13	1	no	—
307	C₂	—	13	1	no	—
308	C₂	—	65	1	no	—
309	C₂	—	65	1	no	—
310	C₂	AGL(1,𝔽₅)×AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	AGL(1,𝔽₅)×AGL(1,𝔽₁₃)
commutator, hypocenter	C₅×C₁₃	C₂×C₃×C₄²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃	C₃×C₄²
prime radical	C₂×D₅×D₁₃⋊C₃	C₂²
cosocle	D₅×D₁₃	C₂³×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
4. C₂×AGL(1,𝔽₅)×#261	C₃	semidirect
5. AGL(1,𝔽₅)×AGL(1,𝔽₁₃)	C₂	direct (N × H)
7. C₂×#63118⋊C₃	C₄	semidirect
8. C₂×#63120⋊C₃	C₄	semidirect
9. C₂×#63122⋊C₃	C₄	semidirect
10. C₂×#63121⋊C₃	C₄	semidirect
11. C₂×AGL(1,𝔽₅)×C₁₃⋊C₃	C₄	semidirect
12. C₂×C₅×AGL(1,𝔽₁₃)	C₄	semidirect
13. D₅×AGL(1,𝔽₁₃)	C₄	semidirect
15. AGL(1,𝔽₅)×D₁₃⋊C₃	C₄	semidirect
17. D₅⋊AGL(1,𝔽₁₃)	C₄	semidirect
23. AGL(1,𝔽₅)×#261	C₂×C₃	semidirect
31. #63118⋊C₃	C₂×C₄	semidirect
32. #63120⋊C₃	C₂×C₄	semidirect
33. #63121⋊C₃	C₂×C₄	semidirect
34. #63122⋊C₃	C₂×C₄	semidirect
35. AGL(1,𝔽₅)×C₁₃⋊C₃	C₂×C₄	semidirect
36. C₅×AGL(1,𝔽₁₃)	C₂×C₄	semidirect
42. C₂×#63118	C₃×C₄	semidirect
43. C₂×#63120	C₃×C₄	semidirect
44. C₂×#63121	C₃×C₄	semidirect
45. C₂×#63122	C₃×C₄	semidirect
46. C₂×C₁₃×AGL(1,𝔽₅)	C₃×C₄	semidirect
47. C₂×C₅×#261	C₃×C₄	semidirect
48. D₅×#261	C₃×C₄	semidirect
50. AGL(1,𝔽₅)×D₁₃	C₃×C₄	semidirect
52. D₅⋊#261	C₃×C₄	semidirect
56. C₂×C₅×C₁₃⋊C₃	C₄²	semidirect
57. C₅⋊(D₁₃⋊C₃)	C₄²	semidirect
59. D₅×C₁₃⋊C₃	C₄²	semidirect
61. C₅×D₁₃⋊C₃	C₄²	semidirect
71. C₂×AGL(1,𝔽₁₃)	AGL(1,𝔽₅)	direct (N × H)
83. #63122	C₂×C₃×C₄	semidirect
84. #63121	C₂×C₃×C₄	semidirect
85. #63120	C₂×C₃×C₄	semidirect
86. C₁₃×AGL(1,𝔽₅)	C₂×C₃×C₄	semidirect
87. #63118	C₂×C₃×C₄	semidirect
88. C₅×#261	C₂×C₃×C₄	semidirect
97. C₅×C₁₃⋊C₃	C₂×C₄²	semidirect
109. AGL(1,𝔽₁₃)	C₂×AGL(1,𝔽₅)	direct (N × H)
112. C₂×C₅×C₁₃	C₃×C₄²	semidirect
113. D₆₅	C₃×C₄²	semidirect
115. C₅×D₁₃	C₃×C₄²	semidirect
117. D₅×C₁₃	C₃×C₄²	semidirect
140. C₂×#261	C₃×AGL(1,𝔽₅)	semidirect
152. C₂×C₁₃⋊C₃	C₄×AGL(1,𝔽₅)	semidirect
155. D₁₃⋊C₃	C₄×AGL(1,𝔽₅)	semidirect
157. C₅×C₁₃	C₂×C₃×C₄²	semidirect
181. #261	C₂×C₃×AGL(1,𝔽₅)	semidirect
196. C₂×AGL(1,𝔽₅)	AGL(1,𝔽₁₃)	direct (N × H)
201. C₁₃⋊C₃	C₂×C₄×AGL(1,𝔽₅)	semidirect
212. C₂×C₁₃	C₃×C₄×AGL(1,𝔽₅)	semidirect
215. D₁₃	C₃×C₄×AGL(1,𝔽₅)	semidirect
240. AGL(1,𝔽₅)	C₂×AGL(1,𝔽₁₃)	direct (N × H)
248. C₁₃	C₂×C₃×C₄×AGL(1,𝔽₅)	semidirect
264. C₂×C₅	C₄×AGL(1,𝔽₁₃)	semidirect
267. D₅	C₄×AGL(1,𝔽₁₃)	semidirect
289. C₅	C₂×C₄×AGL(1,𝔽₁₃)	semidirect
310. C₂	AGL(1,𝔽₅)×AGL(1,𝔽₁₃)	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×D₅⋊AGL(1,𝔽₁₃)	2
C₂×AGL(1,𝔽₅)×D₁₃⋊C₃	2
C₂×D₅×AGL(1,𝔽₁₃)	2
C₂×AGL(1,𝔽₅)×#261	3
AGL(1,𝔽₅)×AGL(1,𝔽₁₃)	2
C₂×C₄×AGL(1,𝔽₁₃)	5
C₂×C₃×C₄×AGL(1,𝔽₅)	13

Subgroups — C2×AGL(1,𝔽5)×AGL(1,𝔽13) #72246799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×AGL(1,𝔽₅)×AGL(1,𝔽₁₃) #72246799