Subgroups — C₂×C₃×#65739 #14416422

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4009	C₂	1	2	yes	maximal
4	C₃×#65739	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3993	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#3992	C₂	1	1	yes	maximal, characteristic
7	C₂×#65739	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
9	C₃×Q₈×AGL(1,𝔽₅)	—	2	4	no	—
10	C₃×Q₈×AGL(1,𝔽₅)	C₂²	1	8	yes	—
11	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
12	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
13	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×#689	C₄	1	2	yes	complemented
18	C₃×D₅×Q₁₆	C₄	1	4	yes	complemented
19	C₃×D₅×Q₁₆	C₂²	1	4	yes	—
20	C₂×C₃×Dic₂₀	C₄	1	1	yes	characteristic, complemented
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4009	C₂²	1	8	yes	—
23	C₃×#3993	C₂²	1	4	yes	—
24	C₃×#3992	C₂²	1	4	yes	—
25	C₂×C₃×#441	—	5	1	no	maximal, Hall
26	C₂×Q₈×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
27	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic
28	C₂×#4009	C₂×C₃	1	2	yes	—
29	#65739	C₂×C₃	1	8	yes	direct product factor
30	C₂×#3993	C₂×C₃	1	1	yes	characteristic
31	C₂×#3992	C₂×C₃	1	1	yes	characteristic
32	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
33	C₂²×C₃×AGL(1,𝔽₅)	D₄	1	2	yes	—
34	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
35	C₃×Q₈×D₅	—	2	2	no	—
36	C₃×Q₈×D₅	—	2	2	no	—
37	C₃×Q₈×D₅	C₂×C₄	1	4	yes	—
38	C₃×Q₈×D₅	C₂³	1	4	yes	—
39	C₂×C₃×C₄×D₅	—	2	2	no	—
40	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×Dic₁₀	—	2	2	no	—
42	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
43	C₂×C₃×#170	—	2	1	no	—
44	C₃×C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
45	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
46	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	4	yes	—
47	C₃×C₄×AGL(1,𝔽₅)	—	2	8	no	—
48	C₃×C₄×AGL(1,𝔽₅)	D₄	1	2	yes	—
49	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
50	C₃×D₅⋊C₈	—	2	1	no	—
51	C₃×D₅⋊C₈	C₂³	1	2	yes	—
52	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
53	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₃×#689	C₂×C₄	1	8	yes	complemented
55	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
56	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
57	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
58	C₃×C₈×D₅	C₂³	1	2	yes	—
59	C₂²×C₃×Q₁₆	—	5	1	no	—
60	C₂×C₃×C₄×Q₈	—	5	2	no	—
61	C₃×#441	—	5	8	no	—
62	C₂×C₃×#106	—	5	1	no	—
63	C₂×C₃×#103	—	5	2	no	—
64	C₂×C₃×#97	—	5	1	no	—
65	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
66	Q₈×AGL(1,𝔽₅)	—	2	4	no	—
67	Q₈×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	—
68	C₂×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
69	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
70	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
71	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
72	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₅×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
74	C₂×#689	C₃×C₄	1	2	yes	complemented
75	D₅×Q₁₆	C₃×C₄	1	4	yes	complemented
76	D₅×Q₁₆	C₂²×C₃	1	4	yes	—
77	C₂×Dic₂₀	C₃×C₄	1	1	yes	characteristic, complemented
78	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
79	#4009	C₂²×C₃	1	8	yes	—
80	#3993	C₂²×C₃	1	4	yes	—
81	#3992	C₂²×C₃	1	4	yes	—
82	C₂×#441	—	5	1	no	Sylow
83	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
84	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
85	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
86	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
87	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	4	yes	—
88	C₃×C₅×Q₈	—	2	2	no	—
89	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×Dic₅	—	2	2	no	—
93	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
94	C₃×C₄×D₅	—	2	4	no	—
95	C₃×C₄×D₅	—	2	4	no	—
96	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
97	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
98	C₃×C₄×D₅	#41	1	1	yes	characteristic
99	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
100	C₃×Dic₁₀	—	2	2	no	—
101	C₃×Dic₁₀	—	2	4	no	—
102	C₃×Dic₁₀	—	2	4	no	—
103	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
104	C₃×#170	—	2	2	no	—
105	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
106	C₃×#168	C₂²×C₄	1	2	yes	—
107	C₂²×C₃×Q₈	—	5	2	no	—
108	C₂×C₃×Q₁₆	—	5	2	no	—
109	C₂×C₃×Q₁₆	—	5	4	no	—
110	C₂×C₃×Q₁₆	—	5	4	no	—
111	C₂×C₃×Q₁₆	—	5	1	no	—
112	C₂×C₃×Q₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
113	C₂²×C₃×C₈	—	5	1	no	—
114	C₂²×C₃×C₈	—	5	1	no	—
115	C₃×C₄×Q₈	—	5	8	no	—
116	C₃×C₄×Q₈	—	10	4	no	—
117	C₂×C₃×C₄⋊C₄	—	5	2	no	—
118	C₂×C₃×C₄⋊C₄	—	10	2	no	—
119	C₂×C₃×C₄²	—	5	1	no	—
120	C₂×C₃×C₄²	—	10	2	no	—
121	C₃×#106	—	5	4	no	—
122	C₃×#103	—	5	8	no	—
123	C₃×#97	—	5	4	no	—
124	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
125	C₂²×AGL(1,𝔽₅)	C₃×D₄	1	2	yes	—
126	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
127	Q₈×D₅	—	2	2	no	—
128	Q₈×D₅	—	2	2	no	—
129	Q₈×D₅	C₂×C₃×C₄	1	4	yes	—
130	Q₈×D₅	C₂³×C₃	1	4	yes	—
131	C₂×C₄×D₅	—	2	2	no	—
132	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
133	C₂×Dic₁₀	—	2	2	no	—
134	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
135	C₂×#170	—	2	1	no	—
136	C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
137	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
138	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
139	C₄×AGL(1,𝔽₅)	—	2	8	no	—
140	C₄×AGL(1,𝔽₅)	C₃×D₄	1	2	yes	—
141	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
142	D₅⋊C₈	—	2	1	no	—
143	D₅⋊C₈	C₂³×C₃	1	2	yes	—
144	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
145	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
146	#689	C₂×C₃×C₄	1	8	yes	complemented
147	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
148	Dic₂₀	C₂×C₃×C₄	1	4	yes	complemented
149	C₈×D₅	C₂×C₃×C₄	1	2	yes	—
150	C₈×D₅	C₂³×C₃	1	2	yes	—
151	C₂²×Q₁₆	—	5	1	no	—
152	C₂×C₄×Q₈	—	5	2	no	—
153	#441	—	5	8	no	—
154	C₂×#106	—	5	1	no	—
155	C₂×#103	—	5	2	no	—
156	C₂×#97	—	5	1	no	—
157	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
158	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
159	C₂×C₃×D₅	#137	1	4	yes	—
160	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
161	C₃×AGL(1,𝔽₅)	—	2	4	no	—
162	C₃×AGL(1,𝔽₅)	—	4	4	no	—
163	C₃×C₄×C₅	—	2	4	no	—
164	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
165	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₃×Dic₅	—	2	4	no	—
167	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
168	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
169	C₂×C₃×Q₈	—	5	4	no	—
170	C₂×C₃×Q₈	—	5	4	no	—
171	C₂×C₃×Q₈	—	5	2	no	—
172	C₂×C₃×Q₈	—	10	2	no	—
173	C₂×C₃×Q₈	—	10	2	no	—
174	C₂×C₃×Q₈	—	10	2	no	—
175	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
176	C₂²×C₃×C₄	—	5	1	no	—
177	C₂²×C₃×C₄	—	5	2	no	—
178	C₂²×C₃×C₄	—	10	2	no	—
179	C₂²×C₃×C₄	—	10	2	no	—
180	C₃×Q₁₆	—	5	8	no	—
181	C₃×Q₁₆	—	5	4	no	—
182	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
183	C₂×C₃×C₈	—	5	1	no	—
184	C₂×C₃×C₈	—	5	2	no	—
185	C₂×C₃×C₈	—	5	2	no	—
186	C₂×C₃×C₈	—	5	2	no	—
187	C₂×C₃×C₈	—	10	1	no	—
188	C₂×C₃×C₈	—	10	1	no	—
189	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
190	C₃×C₄⋊C₄	—	5	4	no	—
191	C₃×C₄⋊C₄	—	10	2	no	—
192	C₃×C₄⋊C₄	—	10	8	no	—
193	C₃×C₄²	—	5	2	no	—
194	C₃×C₄²	—	5	2	no	—
195	C₃×C₄²	—	10	8	no	—
196	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
197	C₂×AGL(1,𝔽₅)	—	2	4	no	—
198	C₂×AGL(1,𝔽₅)	—	2	4	no	—
199	C₂×AGL(1,𝔽₅)	—	4	4	no	—
200	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	4	yes	—
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂×Dic₅	—	2	2	no	—
206	C₂×Dic₅	C₃×#41	1	1	yes	characteristic
207	C₄×D₅	—	2	4	no	—
208	C₄×D₅	—	2	4	no	—
209	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
210	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₄×D₅	C₃×#41	1	1	yes	characteristic
212	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
213	Dic₁₀	—	2	2	no	—
214	Dic₁₀	—	2	4	no	—
215	Dic₁₀	—	2	4	no	—
216	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
217	#170	—	2	2	no	—
218	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
219	#168	C₂²×C₃×C₄	1	2	yes	—
220	C₂²×Q₈	—	5	2	no	—
221	C₂×Q₁₆	—	5	2	no	—
222	C₂×Q₁₆	—	5	4	no	—
223	C₂×Q₁₆	—	5	4	no	—
224	C₂×Q₁₆	—	5	1	no	—
225	C₂×Q₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
226	C₂²×C₈	—	5	1	no	—
227	C₂²×C₈	—	5	1	no	—
228	C₄×Q₈	—	5	8	no	—
229	C₄×Q₈	—	10	4	no	—
230	C₂×C₄⋊C₄	—	5	2	no	—
231	C₂×C₄⋊C₄	—	10	2	no	—
232	C₂×C₄²	—	5	1	no	—
233	C₂×C₄²	—	10	2	no	—
234	#106	—	5	4	no	—
235	#103	—	5	8	no	—
236	#97	—	5	4	no	—
237	C₂×C₃×C₅	#441	1	2	yes	complemented
238	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
239	C₃×D₅	#441	1	2	yes	complemented
240	C₃×D₅	C₂×#137	1	2	yes	—
241	C₂³×C₃	—	5	1	no	—
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	5	4	no	—
244	C₃×Q₈	—	10	4	no	—
245	C₃×Q₈	—	10	4	no	—
246	C₃×Q₈	—	10	2	no	—
247	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	4	yes	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	5	1	no	—
250	C₂×C₃×C₄	—	5	1	no	—
251	C₂×C₃×C₄	—	5	1	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	5	1	no	—
254	C₂×C₃×C₄	—	5	4	no	—
255	C₂×C₃×C₄	—	10	4	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	—	10	4	no	—
258	C₂×C₃×C₄	—	10	2	no	—
259	C₂×C₃×C₄	—	10	4	no	—
260	C₂×C₃×C₄	—	20	4	no	—
261	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₃×C₈	—	5	2	no	—
263	C₃×C₈	—	10	2	no	—
264	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
265	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
266	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
267	C₂×D₅	C₃×#137	1	4	yes	—
268	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
269	AGL(1,𝔽₅)	—	2	4	no	—
270	AGL(1,𝔽₅)	—	4	4	no	—
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
273	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
274	Dic₅	—	2	4	no	—
275	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
276	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
277	C₂×Q₈	—	5	4	no	—
278	C₂×Q₈	—	5	4	no	—
279	C₂×Q₈	—	5	2	no	—
280	C₂×Q₈	—	10	2	no	—
281	C₂×Q₈	—	10	2	no	—
282	C₂×Q₈	—	10	2	no	—
283	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
284	C₂²×C₄	—	5	1	no	—
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	10	2	no	—
287	C₂²×C₄	—	10	2	no	—
288	Q₁₆	—	5	8	no	—
289	Q₁₆	—	5	4	no	—
290	Q₁₆	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
291	C₂×C₈	—	5	1	no	—
292	C₂×C₈	—	5	2	no	—
293	C₂×C₈	—	5	2	no	—
294	C₂×C₈	—	5	2	no	—
295	C₂×C₈	—	10	1	no	—
296	C₂×C₈	—	10	1	no	—
297	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₄⋊C₄	—	5	4	no	—
299	C₄⋊C₄	—	10	2	no	—
300	C₄⋊C₄	—	10	8	no	—
301	C₄²	—	5	2	no	—
302	C₄²	—	5	2	no	—
303	C₄²	—	10	8	no	—
304	C₃×C₅	C₂×#441	1	1	yes	characteristic, complemented, Hall
305	C₂²×C₃	—	5	4	no	—
306	C₂²×C₃	—	5	1	no	—
307	C₂²×C₃	—	5	1	no	—
308	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	5	1	no	—
311	C₃×C₄	—	5	1	no	—
312	C₃×C₄	—	10	4	no	—
313	C₃×C₄	—	10	4	no	—
314	C₃×C₄	—	20	4	no	—
315	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂×C₅	C₃×#441	1	2	yes	complemented
318	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
319	D₅	C₃×#441	1	2	yes	complemented
320	D₅	C₂×C₃×#137	1	2	yes	—
321	C₂³	—	5	1	no	—
322	Q₈	—	2	2	no	—
323	Q₈	—	5	4	no	—
324	Q₈	—	10	4	no	—
325	Q₈	—	10	4	no	—
326	Q₈	—	10	2	no	—
327	Q₈	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	5	1	no	—
330	C₂×C₄	—	5	1	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	1	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	5	4	no	—
335	C₂×C₄	—	10	4	no	—
336	C₂×C₄	—	10	4	no	—
337	C₂×C₄	—	10	4	no	—
338	C₂×C₄	—	10	2	no	—
339	C₂×C₄	—	10	4	no	—
340	C₂×C₄	—	20	4	no	—
341	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₈	—	5	2	no	—
343	C₈	—	10	2	no	—
344	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
345	C₂×C₃	—	5	2	no	—
346	C₂×C₃	—	5	2	no	—
347	C₂×C₃	#65739	1	2	yes	direct product factor
348	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
349	C₅	C₂×C₃×#441	1	1	yes	characteristic, complemented, Sylow
350	C₂²	—	5	4	no	—
351	C₂²	—	5	1	no	—
352	C₂²	—	5	1	no	—
353	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	5	1	no	—
356	C₄	—	5	1	no	—
357	C₄	—	10	4	no	—
358	C₄	—	10	4	no	—
359	C₄	—	20	4	no	—
360	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
362	C₃	C₂×#65739	1	1	yes	characteristic, direct product factor, Sylow
363	C₂	—	5	2	no	—
364	C₂	—	5	2	no	—
365	C₂	C₃×#65739	1	2	yes	direct product factor
366	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×Q₁₆	C₄
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×Q₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#441
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
4. C₃×#65739	C₂	direct (N × H)
7. C₂×#65739	C₃	direct (N × H)
16. C₂×C₃×C₅×Q₁₆	C₄	semidirect
17. C₂×C₃×#689	C₄	semidirect
18. C₃×D₅×Q₁₆	C₄	semidirect
20. C₂×C₃×Dic₂₀	C₄	semidirect
29. #65739	C₂×C₃	direct (N × H)
52. C₃×C₅×Q₁₆	C₂×C₄	semidirect
54. C₃×#689	C₂×C₄	semidirect
56. C₃×Dic₂₀	C₂×C₄	semidirect
73. C₂×C₅×Q₁₆	C₃×C₄	semidirect
74. C₂×#689	C₃×C₄	semidirect
75. D₅×Q₁₆	C₃×C₄	semidirect
77. C₂×Dic₂₀	C₃×C₄	semidirect
112. C₂×C₃×Q₁₆	AGL(1,𝔽₅)	semidirect
144. C₅×Q₁₆	C₂×C₃×C₄	semidirect
146. #689	C₂×C₃×C₄	semidirect
148. Dic₂₀	C₂×C₃×C₄	semidirect
182. C₃×Q₁₆	C₂×AGL(1,𝔽₅)	semidirect
225. C₂×Q₁₆	C₃×AGL(1,𝔽₅)	semidirect
237. C₂×C₃×C₅	#441	semidirect
239. C₃×D₅	#441	semidirect
290. Q₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
304. C₃×C₅	C₂×#441	semidirect
317. C₂×C₅	C₃×#441	semidirect
319. D₅	C₃×#441	semidirect
347. C₂×C₃	#65739	direct (N × H)
349. C₅	C₂×C₃×#441	semidirect
362. C₃	C₂×#65739	direct (N × H)
365. C₂	C₃×#65739	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×Q₈×AGL(1,𝔽₅)	2
C₂×C₃×D₅×Q₁₆	2
C₂×C₃×#4009	2
C₃×#65739	2
C₂×C₃×#3993	2
C₂×C₃×#3992	2
C₂×#65739	3
C₂×C₃×#441	5

Subgroups — C2×C3×#65739 #14416422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65739 #14416422