Subgroups — C₃×#10617369 #14329460

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×AGL(1,𝔽₅)	C₂	1	4	yes	maximal, complemented
2	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic
3	C₃×#65780	C₂	1	4	yes	maximal, complemented
4	C₃×#65779	C₂	1	4	yes	maximal, complemented
5	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
6	#10617369	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×AGL(1,𝔽₅)	C₂²	1	4	yes	—
8	C₂×C₃×D₄×D₅	C₂²	1	4	yes	—
9	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
10	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	8	yes	—
11	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
12	C₃×D₄×AGL(1,𝔽₅)	—	2	16	no	—
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
14	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
15	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	4	yes	—
16	C₃×C₅×#127	C₄	1	1	yes	characteristic, complemented
17	C₃×#4086	C₄	1	4	yes	complemented
18	C₃×#4086	C₄	1	2	yes	complemented
19	C₃×#4020	C₄	1	1	yes	characteristic, complemented
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
22	C₃×#2366	—	5	1	no	maximal, Hall
23	C₂×D₄×AGL(1,𝔽₅)	C₂×C₃	1	4	yes	complemented
24	D₅×#127	C₂×C₃	1	1	yes	characteristic
25	#65780	C₂×C₃	1	4	yes	complemented
26	#65779	C₂×C₃	1	4	yes	complemented
27	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	2	yes	complemented
28	C₂³×C₃×D₅	C₂³	1	4	yes	—
29	C₂²×C₃×AGL(1,𝔽₅)	—	2	16	no	—
30	C₂²×C₃×AGL(1,𝔽₅)	—	4	4	no	—
31	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
32	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
33	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
34	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	complemented
35	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	8	yes	complemented
36	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	complemented
37	C₃×D₄×D₅	—	2	8	no	—
38	C₃×D₄×D₅	—	2	8	no	—
39	C₃×D₄×D₅	—	4	2	no	—
40	C₃×D₄×D₅	—	4	2	no	—
41	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	complemented
42	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	complemented
43	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
45	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	16	no	—
46	C₃×C₂²⋊AGL(1,𝔽₅)	—	4	4	no	—
47	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
48	C₃×C₄⋊AGL(1,𝔽₅)	D₄	1	8	yes	complemented
49	C₃×C₄×AGL(1,𝔽₅)	—	2	8	no	—
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
51	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
52	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂×C₃×#127	—	5	1	no	—
54	C₂×C₃×C₄×D₄	—	5	4	no	—
55	C₃×#390	—	5	4	no	—
56	C₃×#386	—	5	4	no	—
57	C₃×C₄×C₄⋊C₄	—	5	2	no	—
58	C₂³×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
59	C₂×D₄×D₅	C₂²×C₃	1	4	yes	—
60	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
61	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	—
62	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
63	D₄×AGL(1,𝔽₅)	—	2	16	no	—
64	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
65	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
66	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
67	C₅×#127	C₃×C₄	1	1	yes	characteristic, complemented
68	#4086	C₃×C₄	1	4	yes	complemented
69	#4086	C₃×C₄	1	2	yes	complemented
70	#4020	C₃×C₄	1	1	yes	characteristic, complemented
71	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
72	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
73	#2366	—	5	1	no	Sylow
74	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
75	C₂²×C₃×D₅	—	2	8	no	—
76	C₂²×C₃×D₅	—	2	8	no	—
77	C₂²×C₃×D₅	—	2	4	no	—
78	C₂²×C₃×D₅	—	2	4	no	—
79	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
80	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
81	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
82	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
83	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
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	16	no	—
87	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	8	yes	—
88	C₃×C₅×D₄	—	2	8	no	—
89	C₃×C₅×D₄	—	4	2	no	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₃×C₂²⋊D₅	—	2	16	no	—
93	C₃×C₂²⋊D₅	—	4	4	no	—
94	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
96	C₃×D₂₀	—	2	8	no	—
97	C₃×D₂₀	—	4	2	no	—
98	C₃×C₄×D₅	—	2	1	no	—
99	C₃×C₄×D₅	—	2	1	no	—
100	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
101	C₃×C₄×D₅	#41	1	4	yes	—
102	C₂²×C₃×D₄	—	5	4	no	—
103	C₂²×C₃×D₄	—	5	2	no	—
104	C₂³×C₃×C₄	—	5	4	no	—
105	C₃×#127	—	5	2	no	—
106	C₃×#127	—	5	4	no	—
107	C₃×#127	—	5	1	no	—
108	C₃×#127	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
109	C₃×C₄×D₄	—	10	16	no	—
110	C₂×C₃×C₄⋊C₄	—	5	2	no	—
111	C₂×C₃×C₄⋊C₄	—	5	2	no	—
112	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
113	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
114	C₂×C₃×C₄²	—	5	1	no	—
115	C₂×C₃×C₄²	—	5	4	no	—
116	C₃×#95	—	5	4	no	—
117	C₂³×D₅	C₂³×C₃	1	4	yes	—
118	C₂²×AGL(1,𝔽₅)	—	2	16	no	—
119	C₂²×AGL(1,𝔽₅)	—	4	4	no	—
120	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
121	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
122	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
123	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	complemented
124	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	8	yes	complemented
125	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	complemented
126	D₄×D₅	—	2	8	no	—
127	D₄×D₅	—	2	8	no	—
128	D₄×D₅	—	4	2	no	—
129	D₄×D₅	—	4	2	no	—
130	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
131	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	complemented
132	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
134	C₂²⋊AGL(1,𝔽₅)	—	2	16	no	—
135	C₂²⋊AGL(1,𝔽₅)	—	4	4	no	—
136	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
137	C₄⋊AGL(1,𝔽₅)	C₃×D₄	1	8	yes	complemented
138	C₄×AGL(1,𝔽₅)	—	2	8	no	—
139	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
140	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
141	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
142	C₂×#127	—	5	1	no	—
143	C₂×C₄×D₄	—	5	4	no	—
144	#390	—	5	4	no	—
145	#386	—	5	4	no	—
146	C₄×C₄⋊C₄	—	5	2	no	—
147	C₂²×C₃×C₅	—	2	8	no	—
148	C₂²×C₃×C₅	—	2	4	no	—
149	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₃×D₅	—	2	8	no	—
151	C₂×C₃×D₅	—	2	4	no	—
152	C₂×C₃×D₅	—	4	4	no	—
153	C₂×C₃×D₅	—	4	8	no	—
154	C₂×C₃×D₅	—	4	4	no	—
155	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
156	C₂×C₃×D₅	C₂×#41	1	2	yes	—
157	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
159	C₃×AGL(1,𝔽₅)	—	2	8	no	—
160	C₃×AGL(1,𝔽₅)	—	4	4	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
163	C₃×Dic₅	—	2	1	no	—
164	C₃×Dic₅	C₄×D₄	1	4	yes	complemented
165	C₂⁴×C₃	—	5	4	no	—
166	C₂×C₃×D₄	—	5	8	no	—
167	C₂×C₃×D₄	—	5	4	no	—
168	C₂×C₃×D₄	—	5	4	no	—
169	C₂×C₃×D₄	—	5	2	no	—
170	C₂×C₃×D₄	—	10	8	no	—
171	C₂×C₃×D₄	—	10	8	no	—
172	C₂×C₃×D₄	—	20	2	no	—
173	C₂×C₃×D₄	—	20	2	no	—
174	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
175	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
176	C₂²×C₃×C₄	—	5	2	no	—
177	C₂²×C₃×C₄	—	5	4	no	—
178	C₂²×C₃×C₄	—	5	1	no	—
179	C₂²×C₃×C₄	—	5	4	no	—
180	C₂²×C₃×C₄	—	10	16	no	—
181	C₂²×C₃×C₄	—	20	4	no	—
182	C₃×C₄⋊C₄	—	5	8	no	—
183	C₃×C₄⋊C₄	—	10	4	no	—
184	C₃×C₂²⋊C₄	—	10	16	no	—
185	C₃×C₂²⋊C₄	—	20	4	no	—
186	C₃×C₄²	—	5	1	no	—
187	C₃×C₄²	—	5	2	no	—
188	C₃×C₄²	—	10	8	no	—
189	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
190	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
191	C₂²×D₅	—	2	8	no	—
192	C₂²×D₅	—	2	8	no	—
193	C₂²×D₅	—	2	4	no	—
194	C₂²×D₅	—	2	4	no	—
195	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
196	C₂²×D₅	C₂⁴×C₃	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)	—	2	4	no	—
200	C₂×AGL(1,𝔽₅)	—	2	4	no	—
201	C₂×AGL(1,𝔽₅)	—	2	4	no	—
202	C₂×AGL(1,𝔽₅)	—	4	16	no	—
203	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	8	yes	—
204	C₅×D₄	—	2	8	no	—
205	C₅×D₄	—	4	2	no	—
206	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
208	C₂²⋊D₅	—	2	16	no	—
209	C₂²⋊D₅	—	4	4	no	—
210	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
212	D₂₀	—	2	8	no	—
213	D₂₀	—	4	2	no	—
214	C₄×D₅	—	2	1	no	—
215	C₄×D₅	—	2	1	no	—
216	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
217	C₄×D₅	C₃×#41	1	4	yes	—
218	C₂²×D₄	—	5	4	no	—
219	C₂²×D₄	—	5	2	no	—
220	C₂³×C₄	—	5	4	no	—
221	#127	—	5	2	no	—
222	#127	—	5	4	no	—
223	#127	—	5	1	no	—
224	#127	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
225	C₄×D₄	—	10	16	no	—
226	C₂×C₄⋊C₄	—	5	2	no	—
227	C₂×C₄⋊C₄	—	5	2	no	—
228	C₂×C₂²⋊C₄	—	5	8	no	—
229	C₂×C₂²⋊C₄	—	5	4	no	—
230	C₂×C₄²	—	5	1	no	—
231	C₂×C₄²	—	5	4	no	—
232	#95	—	5	4	no	—
233	C₂×C₃×C₅	—	4	4	no	—
234	C₂×C₃×C₅	C₂×C₄×D₄	1	2	yes	—
235	C₂×C₃×C₅	#518	1	1	yes	characteristic
236	C₃×D₅	—	4	4	no	—
237	C₃×D₅	D₄²	1	1	yes	characteristic
238	C₃×D₅	#550	1	2	yes	—
239	C₃×D₅	#559	1	1	yes	characteristic
240	C₂³×C₃	—	5	1	no	—
241	C₂³×C₃	—	5	4	no	—
242	C₂³×C₃	—	10	8	no	—
243	C₂³×C₃	—	10	4	no	—
244	C₂³×C₃	—	10	4	no	—
245	C₂³×C₃	—	10	8	no	—
246	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	4	yes	—
247	C₃×D₄	—	2	8	no	—
248	C₃×D₄	—	4	2	no	—
249	C₃×D₄	—	10	16	no	—
250	C₃×D₄	—	10	8	no	—
251	C₃×D₄	—	20	2	no	—
252	C₃×D₄	—	20	4	no	—
253	C₂×C₃×C₄	—	5	2	no	—
254	C₂×C₃×C₄	—	5	4	no	—
255	C₂×C₃×C₄	—	5	4	no	—
256	C₂×C₃×C₄	—	5	8	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	10	1	no	—
259	C₂×C₃×C₄	—	10	1	no	—
260	C₂×C₃×C₄	—	10	4	no	—
261	C₂×C₃×C₄	—	10	4	no	—
262	C₂×C₃×C₄	—	10	4	no	—
263	C₂×C₃×C₄	—	10	4	no	—
264	C₂×C₃×C₄	—	10	4	no	—
265	C₂×C₃×C₄	—	20	16	no	—
266	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
268	C₂²×C₅	—	2	8	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
271	C₂×D₅	—	2	8	no	—
272	C₂×D₅	—	2	4	no	—
273	C₂×D₅	—	4	4	no	—
274	C₂×D₅	—	4	4	no	—
275	C₂×D₅	—	4	8	no	—
276	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
277	C₂×D₅	C₂×C₃×#41	1	2	yes	—
278	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
280	AGL(1,𝔽₅)	—	2	8	no	—
281	AGL(1,𝔽₅)	—	4	4	no	—
282	C₄×C₅	—	2	1	no	—
283	C₄×C₅	C₃×C₄×D₄	1	4	yes	complemented
284	Dic₅	—	2	1	no	—
285	Dic₅	C₃×C₄×D₄	1	4	yes	complemented
286	C₂⁴	—	5	4	no	—
287	C₂×D₄	—	5	8	no	—
288	C₂×D₄	—	5	4	no	—
289	C₂×D₄	—	5	4	no	—
290	C₂×D₄	—	5	2	no	—
291	C₂×D₄	—	10	8	no	—
292	C₂×D₄	—	10	8	no	—
293	C₂×D₄	—	20	2	no	—
294	C₂×D₄	—	20	2	no	—
295	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
296	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
297	C₂²×C₄	—	5	2	no	—
298	C₂²×C₄	—	5	4	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	4	no	—
301	C₂²×C₄	—	10	16	no	—
302	C₂²×C₄	—	20	4	no	—
303	C₄⋊C₄	—	5	8	no	—
304	C₄⋊C₄	—	10	4	no	—
305	C₂²⋊C₄	—	10	16	no	—
306	C₂²⋊C₄	—	20	4	no	—
307	C₄²	—	5	1	no	—
308	C₄²	—	5	2	no	—
309	C₄²	—	10	8	no	—
310	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
311	C₃×C₅	#2366	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	2	8	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	5	2	no	—
315	C₂²×C₃	—	5	2	no	—
316	C₂²×C₃	—	5	1	no	—
317	C₂²×C₃	—	5	1	no	—
318	C₂²×C₃	—	10	8	no	—
319	C₂²×C₃	—	10	4	no	—
320	C₂²×C₃	—	20	4	no	—
321	C₂²×C₃	—	20	8	no	—
322	C₂²×C₃	—	20	4	no	—
323	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	5	4	no	—
326	C₃×C₄	—	10	8	no	—
327	C₃×C₄	—	10	1	no	—
328	C₃×C₄	—	20	4	no	—
329	C₃×C₄	D₄×AGL(1,𝔽₅)	1	4	yes	complemented
330	C₂×C₅	—	4	4	no	—
331	C₂×C₅	C₂×C₃×C₄×D₄	1	2	yes	—
332	C₂×C₅	C₃×#518	1	1	yes	characteristic
333	D₅	—	4	4	no	—
334	D₅	C₃×D₄²	1	1	yes	characteristic
335	D₅	C₃×#550	1	2	yes	—
336	D₅	C₃×#559	1	1	yes	characteristic
337	C₂³	—	5	1	no	—
338	C₂³	—	5	4	no	—
339	C₂³	—	10	8	no	—
340	C₂³	—	10	4	no	—
341	C₂³	—	10	4	no	—
342	C₂³	—	10	8	no	—
343	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
344	D₄	—	2	8	no	—
345	D₄	—	4	2	no	—
346	D₄	—	10	16	no	—
347	D₄	—	10	8	no	—
348	D₄	—	20	2	no	—
349	D₄	—	20	4	no	—
350	C₂×C₄	—	5	2	no	—
351	C₂×C₄	—	5	4	no	—
352	C₂×C₄	—	5	4	no	—
353	C₂×C₄	—	5	8	no	—
354	C₂×C₄	—	5	1	no	—
355	C₂×C₄	—	10	1	no	—
356	C₂×C₄	—	10	1	no	—
357	C₂×C₄	—	10	4	no	—
358	C₂×C₄	—	10	4	no	—
359	C₂×C₄	—	10	4	no	—
360	C₂×C₄	—	10	4	no	—
361	C₂×C₄	—	10	4	no	—
362	C₂×C₄	—	20	16	no	—
363	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
365	C₂×C₃	—	4	4	no	—
366	C₂×C₃	—	5	1	no	—
367	C₂×C₃	—	5	2	no	—
368	C₂×C₃	—	5	1	no	—
369	C₂×C₃	—	20	4	no	—
370	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	2	yes	—
371	C₂×C₃	#66258	1	1	yes	characteristic
372	C₅	C₃×#2366	1	1	yes	characteristic, complemented, Sylow
373	C₂²	—	2	8	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	5	2	no	—
376	C₂²	—	5	2	no	—
377	C₂²	—	5	1	no	—
378	C₂²	—	5	1	no	—
379	C₂²	—	10	8	no	—
380	C₂²	—	10	4	no	—
381	C₂²	—	20	4	no	—
382	C₂²	—	20	8	no	—
383	C₂²	—	20	4	no	—
384	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	5	4	no	—
387	C₄	—	10	8	no	—
388	C₄	—	10	1	no	—
389	C₄	—	20	4	no	—
390	C₄	C₃×D₄×AGL(1,𝔽₅)	1	4	yes	complemented
391	C₃	#10617369	1	1	yes	characteristic, direct product factor, Sylow
392	C₂	—	4	4	no	—
393	C₂	—	5	1	no	—
394	C₂	—	5	2	no	—
395	C₂	—	5	1	no	—
396	C₂	—	20	4	no	—
397	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
398	C₂	C₃×#66258	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#127	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×D₅×#127	C₂
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×#127	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2366
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×AGL(1,𝔽₅)	C₂	semidirect
3. C₃×#65780	C₂	semidirect
4. C₃×#65779	C₂	semidirect
5. C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
6. #10617369	C₃	direct (N × H)
16. C₃×C₅×#127	C₄	semidirect
17. C₃×#4086	C₄	semidirect
18. C₃×#4086	C₄	semidirect
19. C₃×#4020	C₄	semidirect
23. C₂×D₄×AGL(1,𝔽₅)	C₂×C₃	semidirect
25. #65780	C₂×C₃	semidirect
26. #65779	C₂×C₃	semidirect
27. C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
33. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
34. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
35. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
36. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
41. C₂×C₃×D₂₀	C₂×C₄	semidirect
42. C₂×C₃×D₂₀	C₂×C₄	semidirect
48. C₃×C₄⋊AGL(1,𝔽₅)	D₄	semidirect
50. C₃×C₄²×C₅	C₂×C₄	semidirect
51. C₃×C₄×Dic₅	C₂×C₄	semidirect
52. C₃×C₄×Dic₅	C₂×C₄	semidirect
67. C₅×#127	C₃×C₄	semidirect
68. #4086	C₃×C₄	semidirect
69. #4086	C₃×C₄	semidirect
70. #4020	C₃×C₄	semidirect
108. C₃×#127	AGL(1,𝔽₅)	semidirect
122. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
123. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
124. C₂×C₂²⋊D₅	C₂×C₃×C₄	semidirect
125. C₂×C₂²⋊D₅	C₂×C₃×C₄	semidirect
130. C₂×D₂₀	C₂×C₃×C₄	semidirect
131. C₂×D₂₀	C₂×C₃×C₄	semidirect
137. C₄⋊AGL(1,𝔽₅)	C₃×D₄	semidirect
139. C₄²×C₅	C₂×C₃×C₄	semidirect
140. C₄×Dic₅	C₂×C₃×C₄	semidirect
141. C₄×Dic₅	C₂×C₃×C₄	semidirect
162. C₃×C₄×C₅	C₄×D₄	semidirect
164. C₃×Dic₅	C₄×D₄	semidirect
174. C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	semidirect
175. C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	semidirect
189. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
224. #127	C₃×AGL(1,𝔽₅)	semidirect
283. C₄×C₅	C₃×C₄×D₄	semidirect
285. Dic₅	C₃×C₄×D₄	semidirect
295. C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
296. C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
310. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
311. C₃×C₅	#2366	semidirect
329. C₃×C₄	D₄×AGL(1,𝔽₅)	semidirect
372. C₅	C₃×#2366	semidirect
390. C₄	C₃×D₄×AGL(1,𝔽₅)	semidirect
391. C₃	#10617369	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×D₄×AGL(1,𝔽₅)	2
C₃×D₅×#127	2
C₃×#65780	2
C₃×#65779	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
#10617369	3
C₃×#2366	5

Subgroups — C3×#10617369 #14329460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617369 #14329460