Subgroups — C₃×#10599530 #14298582

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic
2	C₃×#65421	C₂	1	1	yes	maximal, characteristic
3	C₃×#65295	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64777	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64751	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64743	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599530	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×#709	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
14	C₃×#4072	C₂²	1	1	yes	characteristic
15	C₃×#4072	C₂²	1	1	yes	characteristic
16	C₂×C₃×#681	C₂²	1	1	yes	characteristic
17	C₃×C₄×D₂₀	—	2	1	no	—
18	C₃×#4018	C₄	1	2	yes	complemented
19	C₃×C₄²×D₅	C₄	1	2	yes	complemented
20	C₃×C₄×Dic₁₀	—	2	1	no	—
21	C₃×#3956	—	2	1	no	—
22	C₃×#3955	—	2	1	no	—
23	C₃×#3938	—	2	2	no	—
24	C₃×#1827	—	5	1	no	maximal, Hall
25	C₄×#709	C₂×C₃	1	1	yes	characteristic
26	#65421	C₂×C₃	1	1	yes	characteristic
27	#65295	C₂×C₃	1	1	yes	characteristic
28	C₅×#339	C₂×C₃	1	1	yes	characteristic, complemented
29	#64777	C₂×C₃	1	1	yes	characteristic, complemented
30	#64751	C₂×C₃	1	1	yes	characteristic, complemented
31	#64743	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
35	C₃×#709	—	2	1	no	—
36	C₃×#709	—	2	1	no	—
37	C₃×#709	—	2	1	no	—
38	C₃×#709	—	2	1	no	—
39	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	—	2	2	no	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
42	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
43	C₃×C₅×M₁₆	—	2	1	no	—
44	C₃×C₅×M₁₆	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₂²⋊Dic₅	—	2	1	no	—
53	C₃×C₂²⋊Dic₅	—	2	1	no	—
54	C₃×#685	—	2	2	no	—
55	C₃×C₄⋊Dic₅	—	2	1	no	—
56	C₃×C₄⋊Dic₅	—	2	1	no	—
57	C₃×#683	—	2	2	no	—
58	C₃×C₄×Dic₅	—	2	2	no	—
59	C₃×C₄×Dic₅	—	2	1	no	—
60	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
61	C₃×#681	—	2	1	no	—
62	C₃×#681	—	2	1	no	—
63	C₂×C₃×#168	—	2	1	no	—
64	C₃×C₄×#41	—	5	1	no	—
65	C₃×#413	—	5	1	no	—
66	C₃×#410	—	5	1	no	—
67	C₃×#339	—	5	1	no	—
68	C₃×#339	D₅	1	1	yes	characteristic, complemented
69	C₃×H(3,ℤ/4)	—	5	1	no	—
70	C₃×H(3,ℤ/4)	—	5	1	no	—
71	C₂×#709	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
73	C₅×#117	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₄×C₂²⋊D₅	—	2	2	no	—
76	#4072	C₂²×C₃	1	1	yes	characteristic
77	#4072	C₂²×C₃	1	1	yes	characteristic
78	C₂×#681	C₂²×C₃	1	1	yes	characteristic
79	C₄×D₂₀	—	2	1	no	—
80	#4018	C₃×C₄	1	2	yes	complemented
81	C₄²×D₅	C₃×C₄	1	2	yes	complemented
82	C₄×Dic₁₀	—	2	1	no	—
83	#3956	—	2	1	no	—
84	#3955	—	2	1	no	—
85	#3938	—	2	2	no	—
86	#1827	—	5	1	no	Sylow
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₃×D₅	C₂²⋊C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	4	2	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₃×C₂²⋊D₅	—	2	2	no	—
100	C₃×C₂²⋊D₅	—	2	2	no	—
101	C₂×C₃×Dic₅	—	2	2	no	—
102	C₂×C₃×Dic₅	—	4	1	no	—
103	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
104	C₃×D₂₀	—	2	1	no	—
105	C₃×D₂₀	—	2	1	no	—
106	C₃×C₄×D₅	—	2	2	no	—
107	C₃×C₄×D₅	—	2	2	no	—
108	C₃×C₄×D₅	—	4	4	no	—
109	C₃×Dic₁₀	—	2	1	no	—
110	C₃×Dic₁₀	—	2	1	no	—
111	C₃×C₅×C₈	—	4	1	no	—
112	C₃×#168	—	4	1	no	—
113	C₂×C₃×#41	—	5	1	no	—
114	C₂×C₃×M₁₆	—	5	1	no	—
115	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
116	C₃×C₄×Q₈	—	10	1	no	—
117	C₃×C₄×D₄	—	10	1	no	—
118	C₃×C₄×D₄	—	10	2	no	—
119	C₃×#117	—	5	1	no	—
120	C₃×#117	—	5	2	no	—
121	C₃×#117	—	5	1	no	—
122	C₃×#117	C₂×D₅	1	1	yes	characteristic
123	C₂×C₃×C₄²	—	5	2	no	—
124	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
125	C₃×#101	—	10	1	no	—
126	C₃×#100	—	10	1	no	—
127	C₃×#99	—	10	2	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
131	#709	—	2	1	no	—
132	#709	—	2	1	no	—
133	#709	—	2	1	no	—
134	#709	—	2	1	no	—
135	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
136	C₂×C₄×D₅	—	2	2	no	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
138	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
139	C₅×M₁₆	—	2	1	no	—
140	C₅×M₁₆	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₂²⋊C₄	—	2	1	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²⋊Dic₅	—	2	1	no	—
149	C₂²⋊Dic₅	—	2	1	no	—
150	#685	—	2	2	no	—
151	C₄⋊Dic₅	—	2	1	no	—
152	C₄⋊Dic₅	—	2	1	no	—
153	#683	—	2	2	no	—
154	C₄×Dic₅	—	2	2	no	—
155	C₄×Dic₅	—	2	1	no	—
156	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
157	#681	—	2	1	no	—
158	#681	—	2	1	no	—
159	C₂×#168	—	2	1	no	—
160	C₄×#41	—	5	1	no	—
161	#413	—	5	1	no	—
162	#410	—	5	1	no	—
163	#339	—	5	1	no	—
164	#339	C₃×D₅	1	1	yes	characteristic, complemented
165	H(3,ℤ/4)	—	5	1	no	—
166	H(3,ℤ/4)	—	5	1	no	—
167	C₂²×C₃×C₅	—	4	1	no	—
168	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₃×C₅	#123	1	1	yes	characteristic
170	C₂²×C₃×C₅	#123	1	1	yes	characteristic
171	C₂×C₃×D₅	—	2	2	no	—
172	C₂×C₃×D₅	—	4	2	no	—
173	C₃×C₄×C₅	—	2	2	no	—
174	C₃×C₄×C₅	—	4	1	no	—
175	C₃×C₄×C₅	—	8	1	no	—
176	C₃×C₄×C₅	#117	1	1	yes	characteristic
177	C₃×C₄×C₅	#117	1	1	yes	characteristic
178	C₃×C₄×C₅	#123	1	1	yes	characteristic
179	C₃×C₄×C₅	#123	1	1	yes	characteristic
180	C₃×Dic₅	—	2	2	no	—
181	C₃×Dic₅	—	4	2	no	—
182	C₃×Dic₅	—	8	1	no	—
183	C₃×#41	—	10	1	no	—
184	C₃×#41	—	10	1	no	—
185	C₃×#41	—	10	1	no	—
186	C₃×#41	—	10	1	no	—
187	C₂×C₃×Q₈	—	5	1	no	—
188	C₂×C₃×D₄	—	5	2	no	—
189	C₂×C₃×D₄	—	5	1	no	—
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	—	5	2	no	—
192	C₂²×C₃×C₄	—	10	2	no	—
193	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
194	C₃×M₁₆	—	2	1	no	—
195	C₃×M₁₆	—	2	1	no	—
196	C₃×M₁₆	—	10	1	no	—
197	C₃×M₁₆	—	10	1	no	—
198	C₂×C₃×C₈	—	2	1	no	—
199	C₂×C₃×C₈	—	10	1	no	—
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	—	10	2	no	—
202	C₃×C₄⋊C₄	—	10	1	no	—
203	C₃×C₄⋊C₄	—	10	1	no	—
204	C₃×C₂²⋊C₄	—	2	1	no	—
205	C₃×C₂²⋊C₄	—	10	2	no	—
206	C₃×C₂²⋊C₄	—	10	1	no	—
207	C₃×C₂²⋊C₄	—	10	1	no	—
208	C₃×C₄²	—	2	1	no	—
209	C₃×C₄²	—	2	1	no	—
210	C₃×C₄²	—	5	2	no	—
211	C₃×C₄²	—	10	2	no	—
212	C₃×C₄²	—	10	1	no	—
213	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
214	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
215	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂²×D₅	C₃×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
224	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
225	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
226	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
227	C₂²⋊D₅	—	2	2	no	—
228	C₂²⋊D₅	—	2	2	no	—
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	4	1	no	—
231	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
232	D₂₀	—	2	1	no	—
233	D₂₀	—	2	1	no	—
234	C₄×D₅	—	2	2	no	—
235	C₄×D₅	—	2	2	no	—
236	C₄×D₅	—	4	4	no	—
237	Dic₁₀	—	2	1	no	—
238	Dic₁₀	—	2	1	no	—
239	C₅×C₈	—	4	1	no	—
240	#168	—	4	1	no	—
241	C₂×#41	—	5	1	no	—
242	C₂×M₁₆	—	5	1	no	—
243	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
244	C₄×Q₈	—	10	1	no	—
245	C₄×D₄	—	10	1	no	—
246	C₄×D₄	—	10	2	no	—
247	#117	—	5	1	no	—
248	#117	—	5	2	no	—
249	#117	—	5	1	no	—
250	#117	C₂×C₃×D₅	1	1	yes	characteristic
251	C₂×C₄²	—	5	2	no	—
252	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
253	#101	—	10	1	no	—
254	#100	—	10	1	no	—
255	#99	—	10	2	no	—
256	C₂×C₃×C₅	—	2	1	no	—
257	C₂×C₃×C₅	—	2	1	no	—
258	C₂×C₃×C₅	—	2	1	no	—
259	C₂×C₃×C₅	#381	1	1	yes	characteristic
260	C₃×D₅	—	4	2	no	—
261	C₂³×C₃	—	5	2	no	—
262	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
263	C₃×Q₈	—	10	1	no	—
264	C₃×Q₈	—	10	1	no	—
265	C₃×D₄	—	10	2	no	—
266	C₃×D₄	—	10	2	no	—
267	C₃×D₄	—	10	1	no	—
268	C₃×D₄	—	10	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	—	5	2	no	—
274	C₂×C₃×C₄	—	10	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	—	20	4	no	—
278	C₂×C₃×C₄	—	20	1	no	—
279	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
280	C₂×C₃×C₄	#709	1	1	yes	characteristic
281	C₂×C₃×C₄	#709	1	1	yes	characteristic
282	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	#711	1	1	yes	characteristic
284	C₂×C₃×C₄	#713	1	1	yes	characteristic
285	C₃×C₈	—	4	1	no	—
286	C₃×C₈	—	20	1	no	—
287	C₂²×C₅	—	4	1	no	—
288	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₅	C₃×#123	1	1	yes	characteristic
290	C₂²×C₅	C₃×#123	1	1	yes	characteristic
291	C₂×D₅	—	2	2	no	—
292	C₂×D₅	—	4	2	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	1	no	—
295	C₄×C₅	—	8	1	no	—
296	C₄×C₅	C₃×#117	1	1	yes	characteristic
297	C₄×C₅	C₃×#117	1	1	yes	characteristic
298	C₄×C₅	C₃×#123	1	1	yes	characteristic
299	C₄×C₅	C₃×#123	1	1	yes	characteristic
300	Dic₅	—	2	2	no	—
301	Dic₅	—	4	2	no	—
302	Dic₅	—	8	1	no	—
303	#41	—	10	1	no	—
304	#41	—	10	1	no	—
305	#41	—	10	1	no	—
306	#41	—	10	1	no	—
307	C₂×Q₈	—	5	1	no	—
308	C₂×D₄	—	5	2	no	—
309	C₂×D₄	—	5	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	5	2	no	—
312	C₂²×C₄	—	10	2	no	—
313	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
314	M₁₆	—	2	1	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	10	1	no	—
317	M₁₆	—	10	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	10	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	10	2	no	—
322	C₄⋊C₄	—	10	1	no	—
323	C₄⋊C₄	—	10	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	10	2	no	—
326	C₂²⋊C₄	—	10	1	no	—
327	C₂²⋊C₄	—	10	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	5	2	no	—
331	C₄²	—	10	2	no	—
332	C₄²	—	10	1	no	—
333	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
334	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
335	C₃×C₅	#1827	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	4	1	no	—
337	C₂²×C₃	—	10	2	no	—
338	C₂²×C₃	—	20	2	no	—
339	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₃	#4029	1	1	yes	characteristic
341	C₂²×C₃	#4040	1	1	yes	characteristic
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	4	1	no	—
344	C₃×C₄	—	8	1	no	—
345	C₃×C₄	—	10	2	no	—
346	C₃×C₄	—	20	2	no	—
347	C₃×C₄	—	40	1	no	—
348	C₃×C₄	#4018	1	1	yes	characteristic
349	C₃×C₄	#4029	1	1	yes	characteristic
350	C₃×C₄	#4038	1	1	yes	characteristic
351	C₃×C₄	#4040	1	1	yes	characteristic
352	C₂×C₅	—	2	1	no	—
353	C₂×C₅	—	2	1	no	—
354	C₂×C₅	—	2	1	no	—
355	C₂×C₅	C₃×#381	1	1	yes	characteristic
356	D₅	—	4	2	no	—
357	C₂³	—	5	2	no	—
358	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
359	Q₈	—	10	1	no	—
360	Q₈	—	10	1	no	—
361	D₄	—	10	2	no	—
362	D₄	—	10	2	no	—
363	D₄	—	10	1	no	—
364	D₄	—	10	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	5	2	no	—
370	C₂×C₄	—	10	2	no	—
371	C₂×C₄	—	10	2	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	20	4	no	—
374	C₂×C₄	—	20	1	no	—
375	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
376	C₂×C₄	C₃×#709	1	1	yes	characteristic
377	C₂×C₄	C₃×#709	1	1	yes	characteristic
378	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
379	C₂×C₄	C₃×#711	1	1	yes	characteristic
380	C₂×C₄	C₃×#713	1	1	yes	characteristic
381	C₈	—	4	1	no	—
382	C₈	—	20	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	20	2	no	—
387	C₂×C₃	#64953	1	1	yes	characteristic
388	C₅	C₃×#1827	1	1	yes	characteristic, complemented, Sylow
389	C₂²	—	4	1	no	—
390	C₂²	—	10	2	no	—
391	C₂²	—	20	2	no	—
392	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
393	C₂²	C₃×#4029	1	1	yes	characteristic
394	C₂²	C₃×#4040	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	8	1	no	—
398	C₄	—	10	2	no	—
399	C₄	—	20	2	no	—
400	C₄	—	40	1	no	—
401	C₄	C₃×#4018	1	1	yes	characteristic
402	C₄	C₃×#4029	1	1	yes	characteristic
403	C₄	C₃×#4038	1	1	yes	characteristic
404	C₄	C₃×#4040	1	1	yes	characteristic
405	C₃	#10599530	1	1	yes	characteristic, direct product factor, Sylow
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	20	2	no	—
410	C₂	C₃×#64953	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#4038
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#339	C₂
socle	C₂×C₃×C₅	#381
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#339	D₅
hypocenter	C₅	C₃×#1827
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#339

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#339	C₂	semidirect
5. C₃×#64777	C₂	semidirect
6. C₃×#64751	C₂	semidirect
7. C₃×#64743	C₂	semidirect
8. #10599530	C₃	direct (N × H)
18. C₃×#4018	C₄	semidirect
19. C₃×C₄²×D₅	C₄	semidirect
28. C₅×#339	C₂×C₃	semidirect
29. #64777	C₂×C₃	semidirect
30. #64751	C₂×C₃	semidirect
31. #64743	C₂×C₃	semidirect
68. C₃×#339	D₅	semidirect
80. #4018	C₃×C₄	semidirect
81. C₄²×D₅	C₃×C₄	semidirect
164. #339	C₃×D₅	semidirect
335. C₃×C₅	#1827	semidirect
388. C₅	C₃×#1827	semidirect
405. C₃	#10599530	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×#709	2
C₃×#65421	2
C₃×#65295	2
C₃×C₅×#339	2
C₃×#64777	2
C₃×#64751	2
C₃×#64743	2
#10599530	3
C₃×#1827	5

Subgroups — C3×#10599530 #14298582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599530 #14298582