Subgroups — C₃×#11746527 #72260248

Order 2880.

548 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#91989	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×#208	C₂	1	1	yes	maximal, characteristic
4	C₃×#64900	—	3	1	no	maximal
5	#11746527	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²×AGL(1,𝔽₅)	—	2	1	no	—
7	C₂×C₃²×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₃×#6763	—	2	1	no	—
9	C₃×C₄⋊ΓL(1,𝔽₁₆)	C₄	1	2	yes	complemented
10	C₃×C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
11	C₃²×C₄×AGL(1,𝔽₅)	—	2	1	no	—
12	C₃²×C₄×AGL(1,𝔽₅)	C₄	1	2	yes	complemented
13	C₃×#6710	C₄	1	1	yes	characteristic, complemented
14	C₃×C₅×#208	C₄	1	1	yes	characteristic, complemented
15	C₃×#6649	—	2	1	no	—
16	C₃×D₅×C₃⋊C₈	—	2	1	no	—
17	C₃×#4523	—	5	1	no	maximal, Hall
18	#91989	C₂×C₃	1	1	yes	characteristic
19	C₃×#4130	—	3	1	no	—
20	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
21	C₂×C₃×C₄×AGL(1,𝔽₅)	D₃	1	1	yes	characteristic
22	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
23	C₃×D₅×M₁₆	—	3	1	no	—
24	D₅×#208	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₃²×D₅	D₄	1	1	yes	characteristic
26	C₂×C₃×ΓL(1,𝔽₁₆)	—	2	2	no	—
27	C₂×C₃²×AGL(1,𝔽₅)	—	2	4	no	—
28	C₂×C₃²×AGL(1,𝔽₅)	—	2	2	no	—
29	C₂×C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃²×Dic₅	Q₈	1	1	yes	characteristic
31	C₃²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
32	C₃²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
33	C₃²×C₄×D₅	D₄	1	1	yes	characteristic
34	C₃²×C₄×D₅	D₄	1	1	yes	characteristic
35	C₃×C₃⋊#168	—	2	1	no	—
36	C₃×C₅×C₃⋊C₈	—	2	1	no	—
37	#64900	—	3	1	no	Hall
38	C₂×C₃²×C₄²	—	5	1	no	—
39	C₃×#926	—	5	1	no	—
40	C₂×C₃×#208	—	5	1	no	—
41	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
42	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
43	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
44	C₂×C₃×C₄×D₅	—	2	1	no	—
45	C₂×C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
47	#6763	—	2	1	no	—
48	C₄⋊ΓL(1,𝔽₁₆)	C₃×C₄	1	2	yes	complemented
49	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
50	C₃×C₂²⋊AGL(1,𝔽₅)	—	6	1	no	—
51	C₃×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
52	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
53	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
54	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
55	C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
56	C₃×C₄×AGL(1,𝔽₅)	—	6	1	no	—
57	C₃×C₄×AGL(1,𝔽₅)	Dic₃	1	2	yes	complemented
58	C₃×C₄×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	complemented
59	C₃×C₅×M₁₆	—	3	1	no	—
60	#6710	C₃×C₄	1	1	yes	characteristic, complemented
61	C₅×#208	C₃×C₄	1	1	yes	characteristic, complemented
62	C₃×#681	—	3	1	no	—
63	C₃×#676	—	6	1	no	—
64	C₃×C₈×D₅	—	6	1	no	—
65	#6649	—	2	1	no	—
66	D₅×C₃⋊C₈	—	2	1	no	—
67	C₃×#339	—	15	1	no	—
68	#4523	—	5	1	no	—
69	C₂²×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₃²×D₅	—	2	2	no	—
71	C₂×C₃²×D₅	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₃²×D₅	C₂²⋊C₄	1	1	yes	characteristic
73	C₃×ΓL(1,𝔽₁₆)	—	4	2	no	—
74	C₃²×AGL(1,𝔽₅)	—	2	4	no	—
75	C₃²×C₄×C₅	C₄²	1	1	yes	characteristic
76	C₃²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₃²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
78	C₃²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
79	#4130	—	3	1	no	—
80	C₂×C₄×AGL(1,𝔽₅)	C₃×D₃	1	1	yes	characteristic
81	D₅×M₁₆	—	3	1	no	—
82	C₂²×C₃²×C₄	—	5	1	no	—
83	C₂²×C₃²×C₄	—	10	1	no	—
84	C₃²×C₄²	—	5	2	no	—
85	C₃²×C₄²	—	10	1	no	—
86	C₃×#217	—	10	1	no	—
87	C₃×C₄⋊Dic₃	—	5	2	no	—
88	C₃×C₄×Dic₃	—	10	1	no	—
89	C₃×#208	—	5	1	no	—
90	C₃×#208	—	10	1	no	—
91	C₃×#208	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
92	C₂×C₃×C₃⋊C₈	—	10	1	no	—
93	C₂²×C₃×D₅	—	2	1	no	—
94	C₂²×C₃×D₅	#67	1	1	yes	characteristic
95	C₂²×C₃×D₅	C₃×D₄	1	1	yes	characteristic
96	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
97	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
98	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
99	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
100	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
101	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
102	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
103	C₂×C₃×AGL(1,𝔽₅)	—	6	2	no	—
104	C₂×C₃×C₄×C₅	—	2	1	no	—
105	C₂×C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
107	C₂×C₃×Dic₅	—	2	1	no	—
108	C₂×C₃×Dic₅	Dic₆	1	1	yes	characteristic
109	C₂×C₃×Dic₅	C₃×Q₈	1	1	yes	characteristic
110	C₃×C₄×D₅	—	2	1	no	—
111	C₃×C₄×D₅	—	2	1	no	—
112	C₃×C₄×D₅	—	2	1	no	—
113	C₃×C₄×D₅	—	2	1	no	—
114	C₃×C₄×D₅	C₄×D₃	1	1	yes	characteristic
115	C₃×C₄×D₅	D₁₂	1	1	yes	characteristic
116	C₃×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
117	C₃×C₄×D₅	#67	1	1	yes	characteristic
118	C₃×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
119	C₃×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₃×C₄×D₅	C₃×D₄	1	1	yes	characteristic
121	C₃×C₄×D₅	C₃×D₄	1	1	yes	characteristic
122	C₃×C₅×C₈	—	6	1	no	—
123	C₃⋊#168	—	2	1	no	—
124	C₃×#168	—	6	1	no	—
125	C₅×C₃⋊C₈	—	2	1	no	—
126	C₂×C₃×M₁₆	—	15	1	no	—
127	C₃×#117	—	15	1	no	—
128	C₂×C₃×C₄²	—	5	1	no	—
129	C₂×C₃×C₄²	—	5	1	no	—
130	C₂×C₃×C₄²	—	10	1	no	—
131	#926	—	5	1	no	—
132	C₂×#208	—	5	1	no	—
133	C₂×C₃²×C₅	—	2	1	no	—
134	C₂×C₃²×C₅	#95	1	1	yes	characteristic
135	C₃²×D₅	—	2	1	no	—
136	C₃²×D₅	#104	1	2	yes	—
137	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
138	C₂×C₄×D₅	C₂×C₃×D₃	1	1	yes	characteristic
139	C₂²⋊AGL(1,𝔽₅)	—	6	1	no	—
140	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
141	C₄×AGL(1,𝔽₅)	—	2	1	no	—
142	C₄×AGL(1,𝔽₅)	—	6	1	no	—
143	C₄×AGL(1,𝔽₅)	C₃×Dic₃	1	2	yes	complemented
144	C₅×M₁₆	—	3	1	no	—
145	#681	—	3	1	no	—
146	#676	—	6	1	no	—
147	C₈×D₅	—	6	1	no	—
148	C₂³×C₃²	—	5	1	no	—
149	C₂×C₃²×C₄	—	5	1	no	—
150	C₂×C₃²×C₄	—	5	1	no	—
151	C₂×C₃²×C₄	—	5	1	no	—
152	C₂×C₃²×C₄	—	5	1	no	—
153	C₂×C₃²×C₄	—	5	1	no	—
154	C₂×C₃²×C₄	—	10	2	no	—
155	C₂×C₃²×C₄	—	10	4	no	—
156	C₂×C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
157	C₂×C₃×Dic₃	—	10	2	no	—
158	C₃×C₃⋊C₈	—	2	1	no	—
159	C₃×C₃⋊C₈	—	10	1	no	—
160	#339	—	15	1	no	Sylow
161	C₂²×C₃×C₅	—	2	1	no	—
162	C₂²×C₃×C₅	Dic₃⋊C₄	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₃×D₅	—	2	4	no	—
165	C₂×C₃×D₅	—	2	2	no	—
166	C₂×C₃×D₅	—	2	2	no	—
167	C₂×C₃×D₅	—	2	1	no	—
168	C₂×C₃×D₅	—	2	1	no	—
169	C₂×C₃×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
170	C₂×C₃×D₅	#217	1	1	yes	characteristic
171	C₂×C₃×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₃×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
173	ΓL(1,𝔽₁₆)	—	4	2	no	—
174	C₃×AGL(1,𝔽₅)	—	2	8	no	—
175	C₃×AGL(1,𝔽₅)	—	2	4	no	—
176	C₃×AGL(1,𝔽₅)	—	2	4	no	—
177	C₃×AGL(1,𝔽₅)	—	12	2	no	—
178	C₃×C₄×C₅	—	2	1	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
181	C₃×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
182	C₃×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
183	C₃×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
184	C₃×Dic₅	—	2	1	no	—
185	C₃×Dic₅	—	2	1	no	—
186	C₃×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
187	C₃×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
188	C₃×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
189	C₃×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×C₃×C₄	—	5	1	no	—
191	C₂²×C₃×C₄	—	5	1	no	—
192	C₂²×C₃×C₄	—	10	1	no	—
193	C₂²×C₃×C₄	—	10	1	no	—
194	C₂²×C₃×C₄	—	10	1	no	—
195	C₂²×C₃×C₄	—	10	2	no	—
196	C₃×M₁₆	—	3	1	no	—
197	C₃×M₁₆	—	15	1	no	—
198	C₃×M₁₆	—	30	1	no	—
199	C₂×C₃×C₈	—	30	1	no	—
200	C₃×C₄⋊C₄	—	15	2	no	—
201	C₃×C₂²⋊C₄	—	30	1	no	—
202	C₃×C₄²	—	5	2	no	—
203	C₃×C₄²	—	5	2	no	—
204	C₃×C₄²	—	10	2	no	—
205	C₃×C₄²	—	10	1	no	—
206	C₃×C₄²	—	10	1	no	—
207	C₃×C₄²	—	10	2	no	—
208	C₃×C₄²	—	30	1	no	—
209	#217	—	10	1	no	—
210	C₄⋊Dic₃	—	5	2	no	—
211	C₄×Dic₃	—	10	1	no	—
212	#208	—	5	1	no	—
213	#208	—	10	1	no	—
214	#208	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
215	C₂×C₃⋊C₈	—	10	1	no	—
216	C₃²×C₅	#339	1	1	yes	characteristic, complemented, Hall
217	C₂²×D₅	C₃×#67	1	1	yes	characteristic
218	C₂×AGL(1,𝔽₅)	—	2	4	no	—
219	C₂×AGL(1,𝔽₅)	—	2	2	no	—
220	C₂×AGL(1,𝔽₅)	—	6	2	no	—
221	C₂×C₄×C₅	C₃×C₄×D₃	1	1	yes	characteristic
222	C₂×Dic₅	C₃×Dic₆	1	1	yes	characteristic
223	C₄×D₅	C₃×C₄×D₃	1	1	yes	characteristic
224	C₄×D₅	C₃×D₁₂	1	1	yes	characteristic
225	C₄×D₅	C₂×C₃×Dic₃	1	1	yes	characteristic
226	C₄×D₅	C₃×#67	1	1	yes	characteristic
227	C₅×C₈	—	6	1	no	—
228	#168	—	6	1	no	—
229	C₂²×C₃²	—	5	1	no	—
230	C₂²×C₃²	—	5	1	no	—
231	C₂²×C₃²	—	10	2	no	—
232	C₂²×C₃²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
233	C₃²×C₄	—	5	1	no	—
234	C₃²×C₄	—	5	1	no	—
235	C₃²×C₄	—	10	4	no	—
236	C₃²×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
237	C₃²×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
238	C₃×Dic₃	—	20	2	no	—
239	C₂×M₁₆	—	15	1	no	—
240	#117	—	15	1	no	—
241	C₂×C₄²	—	5	1	no	—
242	C₂×C₃×C₅	—	2	2	no	—
243	C₂×C₃×C₅	—	2	1	no	—
244	C₂×C₃×C₅	—	2	1	no	—
245	C₂×C₃×C₅	—	2	1	no	—
246	C₂×C₃×C₅	C₃⋊#95	1	1	yes	characteristic
247	C₂×C₃×C₅	C₃×#95	1	1	yes	characteristic
248	C₃×D₅	—	2	2	no	—
249	C₃×D₅	—	2	1	no	—
250	C₃×D₅	—	2	1	no	—
251	C₃×D₅	—	2	2	no	—
252	C₃×D₅	#805	1	2	yes	—
253	C₃×D₅	C₃×#104	1	2	yes	—
254	C₂³×C₃	—	5	1	no	—
255	C₂³×C₃	—	5	1	no	—
256	C₂³×C₃	—	10	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	5	1	no	—
259	C₂×C₃×C₄	—	5	1	no	—
260	C₂×C₃×C₄	—	5	1	no	—
261	C₂×C₃×C₄	—	5	1	no	—
262	C₂×C₃×C₄	—	5	1	no	—
263	C₂×C₃×C₄	—	5	1	no	—
264	C₂×C₃×C₄	—	5	1	no	—
265	C₂×C₃×C₄	—	5	1	no	—
266	C₂×C₃×C₄	—	5	1	no	—
267	C₂×C₃×C₄	—	5	1	no	—
268	C₂×C₃×C₄	—	10	1	no	—
269	C₂×C₃×C₄	—	10	1	no	—
270	C₂×C₃×C₄	—	10	1	no	—
271	C₂×C₃×C₄	—	10	1	no	—
272	C₂×C₃×C₄	—	10	1	no	—
273	C₂×C₃×C₄	—	10	2	no	—
274	C₂×C₃×C₄	—	10	2	no	—
275	C₂×C₃×C₄	—	10	4	no	—
276	C₂×C₃×C₄	—	10	4	no	—
277	C₂×C₃×C₄	—	10	4	no	—
278	C₂×C₃×C₄	—	10	8	no	—
279	C₂×C₃×C₄	—	30	2	no	—
280	C₂×C₃×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
282	C₂×Dic₃	—	10	2	no	—
283	C₃×C₈	—	6	1	no	—
284	C₃×C₈	—	30	1	no	—
285	C₃⋊C₈	—	2	1	no	—
286	C₃⋊C₈	—	10	1	no	—
287	C₂²×C₅	C₃×Dic₃⋊C₄	1	1	yes	characteristic
288	C₂×D₅	—	2	2	no	—
289	C₂×D₅	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
290	C₂×D₅	C₃×#217	1	1	yes	characteristic
291	AGL(1,𝔽₅)	—	2	4	no	—
292	AGL(1,𝔽₅)	—	12	2	no	—
293	C₄×C₅	C₃×C₄×Dic₃	1	1	yes	characteristic
294	C₄×C₅	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
295	Dic₅	C₃×Dic₃⋊C₄	1	1	yes	characteristic
296	Dic₅	C₃×C₄⋊Dic₃	1	1	yes	characteristic
297	C₂×C₃²	—	2	1	no	—
298	C₂×C₃²	—	5	2	no	—
299	C₂×C₃²	—	10	1	no	—
300	C₂×C₃²	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	10	1	no	—
303	M₁₆	—	3	1	no	—
304	M₁₆	—	15	1	no	—
305	M₁₆	—	30	1	no	—
306	C₂×C₈	—	30	1	no	—
307	C₄⋊C₄	—	15	2	no	—
308	C₂²⋊C₄	—	30	1	no	—
309	C₄²	—	5	2	no	—
310	C₄²	—	10	1	no	—
311	C₄²	—	30	1	no	—
312	C₃×C₅	—	2	1	no	—
313	C₃×C₅	#4523	1	1	yes	characteristic, complemented
314	C₃×C₅	C₃×#339	1	1	yes	characteristic, complemented
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	5	1	no	—
317	C₂²×C₃	—	5	1	no	—
318	C₂²×C₃	—	5	1	no	—
319	C₂²×C₃	—	5	1	no	—
320	C₂²×C₃	—	10	1	no	—
321	C₂²×C₃	—	10	1	no	—
322	C₂²×C₃	—	10	2	no	—
323	C₂²×C₃	—	10	2	no	—
324	C₂²×C₃	—	10	4	no	—
325	C₂²×C₃	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₂²×C₃	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	5	1	no	—
330	C₃×C₄	—	5	1	no	—
331	C₃×C₄	—	5	1	no	—
332	C₃×C₄	—	5	1	no	—
333	C₃×C₄	—	10	1	no	—
334	C₃×C₄	—	10	1	no	—
335	C₃×C₄	—	10	8	no	—
336	C₃×C₄	—	10	4	no	—
337	C₃×C₄	—	10	4	no	—
338	C₃×C₄	—	60	2	no	—
339	C₃×C₄	Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
340	C₃×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
341	C₃×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₃×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
343	Dic₃	—	20	2	no	—
344	C₂×C₅	—	2	1	no	—
345	C₂×C₅	C₃×C₃⋊#95	1	1	yes	characteristic
346	D₅	—	2	1	no	—
347	D₅	C₃×#805	1	2	yes	—
348	C₃²	#64900	1	1	yes	characteristic, complemented, Sylow
349	C₂³	—	5	1	no	—
350	C₂×C₄	—	5	1	no	—
351	C₂×C₄	—	5	1	no	—
352	C₂×C₄	—	5	1	no	—
353	C₂×C₄	—	5	1	no	—
354	C₂×C₄	—	5	1	no	—
355	C₂×C₄	—	10	2	no	—
356	C₂×C₄	—	10	4	no	—
357	C₂×C₄	—	30	2	no	—
358	C₂×C₄	C₃×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₈	—	6	1	no	—
360	C₈	—	30	1	no	—
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	5	2	no	—
366	C₂×C₃	—	5	2	no	—
367	C₂×C₃	—	10	2	no	—
368	C₂×C₃	—	10	2	no	—
369	C₂×C₃	—	10	1	no	—
370	C₂×C₃	—	10	1	no	—
371	C₂×C₃	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
372	C₂×C₃	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
373	C₅	C₃×#4523	1	1	yes	characteristic, complemented, Sylow
374	C₂²	—	5	1	no	—
375	C₂²	—	5	1	no	—
376	C₂²	—	10	2	no	—
377	C₂²	C₃×Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₄	—	5	1	no	—
379	C₄	—	5	1	no	—
380	C₄	—	10	4	no	—
381	C₄	—	60	2	no	—
382	C₄	C₃×Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₄	C₃×(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₃	—	2	1	no	—
385	C₃	#11746527	1	1	yes	characteristic, direct product factor
386	C₃	C₃×#64900	1	1	yes	characteristic, complemented
387	C₂	—	2	1	no	—
388	C₂	—	5	2	no	—
389	C₂	—	10	1	no	—
390	C₂	C₃×(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₃×C₄²
Frattini	C₂×C₄	C₃×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃²×C₄×C₅	C₂×C₄
socle	C₂×C₃²×C₅	#95
prime radical	C₂²×C₃²×D₅	D₄
cosocle	C₂×C₃×C₄×D₅	C₂²×C₃
hypercenter	C₂×C₃×C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₃×#339
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
5. #11746527	C₃	direct (N × H)
9. C₃×C₄⋊ΓL(1,𝔽₁₆)	C₄	semidirect
12. C₃²×C₄×AGL(1,𝔽₅)	C₄	semidirect
13. C₃×#6710	C₄	semidirect
14. C₃×C₅×#208	C₄	semidirect
48. C₄⋊ΓL(1,𝔽₁₆)	C₃×C₄	semidirect
57. C₃×C₄×AGL(1,𝔽₅)	Dic₃	semidirect
58. C₃×C₄×AGL(1,𝔽₅)	C₃×C₄	semidirect
60. #6710	C₃×C₄	semidirect
61. C₅×#208	C₃×C₄	semidirect
91. C₃×#208	AGL(1,𝔽₅)	semidirect
143. C₄×AGL(1,𝔽₅)	C₃×Dic₃	semidirect
214. #208	C₃×AGL(1,𝔽₅)	semidirect
216. C₃²×C₅	#339	semidirect
313. C₃×C₅	#4523	semidirect
314. C₃×C₅	C₃×#339	semidirect
348. C₃²	#64900	semidirect
373. C₅	C₃×#4523	semidirect
385. C₃	#11746527	direct (N × H)
386. C₃	C₃×#64900	semidirect

Maximal subgroups

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

subgroup	index
C₃×#91989	2
C₂×C₃²×C₄×AGL(1,𝔽₅)	2
C₃×D₅×#208	2
C₃×#64900	3
#11746527	3
C₃×#4523	5

Subgroups — C3×#11746527 #72260248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#11746527 #72260248