Subgroups — C₃×#10600681 #14296009

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3957	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65291	C₂	1	1	yes	maximal, characteristic
6	C₃×#64778	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64752	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600681	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	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×#681	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
16	C₃×#4047	—	2	2	no	—
17	C₃×#4047	C₄	1	4	yes	complemented
18	C₂×C₃×#676	—	2	1	no	—
19	C₂×C₃×C₈×D₅	—	2	1	no	—
20	C₃×C₅×#97	—	2	1	no	—
21	C₃×C₄×C₅×C₈	—	2	1	no	—
22	C₃×#3957	C₄	1	4	yes	complemented
23	C₃×#3947	—	2	2	no	—
24	C₃×#3942	C₄	1	2	yes	complemented
25	C₃×#3941	C₄	1	2	yes	complemented
26	C₃×#1765	—	5	1	no	maximal, Hall
27	C₂×#4047	C₂×C₃	1	1	yes	characteristic
28	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×#3957	C₂×C₃	1	1	yes	characteristic
30	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
31	#65291	C₂×C₃	1	1	yes	characteristic
32	#64778	C₂×C₃	1	1	yes	characteristic, complemented
33	#64752	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
36	C₂²×C₃×Dic₅	—	2	1	no	—
37	C₃×#709	—	2	1	no	—
38	C₃×#709	—	2	1	no	—
39	C₃×#709	C₂×C₄	1	2	yes	—
40	C₃×#709	C₂×C₄	1	2	yes	—
41	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	—	2	1	no	—
43	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×M₁₆	—	2	1	no	—
45	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
49	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄×Dic₅	—	2	1	no	—
55	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
56	C₃×#681	—	2	1	no	—
57	C₃×#681	C₂×C₄	1	2	yes	—
58	C₂×C₃×#168	—	2	1	no	—
59	C₂×C₃×#168	—	2	1	no	—
60	C₂×C₃×#168	—	2	1	no	—
61	C₂×C₃×#168	C₂×C₄	1	2	yes	—
62	C₃×#676	—	2	4	no	—
63	C₃×C₈×D₅	—	2	4	no	—
64	C₂×C₃×#131	—	5	1	no	—
65	C₂×C₃×#104	—	5	1	no	—
66	C₃×#416	—	5	1	no	—
67	C₃×#405	D₅	1	1	yes	characteristic, complemented
68	C₂×C₃×#97	—	5	1	no	—
69	C₃×#341	—	5	1	no	—
70	C₃×#339	—	5	1	no	—
71	C₂×#709	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₅×#117	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×#681	C₂²×C₃	1	1	yes	characteristic
77	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
78	#4047	—	2	2	no	—
79	#4047	C₃×C₄	1	4	yes	complemented
80	C₂×#676	—	2	1	no	—
81	C₂×C₈×D₅	—	2	1	no	—
82	C₅×#97	—	2	1	no	—
83	C₄×C₅×C₈	—	2	1	no	—
84	#3957	C₃×C₄	1	4	yes	complemented
85	#3947	—	2	2	no	—
86	#3942	C₃×C₄	1	2	yes	complemented
87	#3941	C₃×C₄	1	2	yes	complemented
88	#1765	—	5	1	no	Sylow
89	C₂³×C₃×C₅	#41	1	1	yes	characteristic
90	C₂²×C₃×D₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₃×C₂²⋊D₅	—	2	2	no	—
99	C₃×C₂²⋊D₅	—	2	2	no	—
100	C₂×C₃×Dic₅	—	2	1	no	—
101	C₂×C₃×Dic₅	—	2	2	no	—
102	C₂×C₃×Dic₅	—	4	2	no	—
103	C₃×D₂₀	—	2	1	no	—
104	C₃×D₂₀	C₄²	1	2	yes	—
105	C₃×C₄×D₅	—	2	2	no	—
106	C₃×C₄×D₅	—	2	2	no	—
107	C₃×Dic₁₀	—	2	1	no	—
108	C₃×Dic₁₀	C₄²	1	2	yes	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
111	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
112	C₃×#168	—	2	2	no	—
113	C₃×#168	—	2	2	no	—
114	C₂×C₃×#41	—	5	1	no	—
115	C₃×#131	—	5	4	no	—
116	C₃×#131	—	10	2	no	—
117	C₂×C₃×M₁₆	—	5	1	no	—
118	C₂×C₃×M₁₆	—	10	1	no	—
119	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	—	5	1	no	—
121	C₂²×C₃×C₈	—	10	1	no	—
122	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
123	C₃×#117	C₂×D₅	1	1	yes	characteristic
124	C₂×C₃×C₄²	—	5	1	no	—
125	C₃×#104	—	5	4	no	—
126	C₃×#103	—	5	2	no	—
127	C₃×#102	—	5	2	no	—
128	C₃×#97	—	2	1	no	—
129	C₃×#97	—	10	2	no	—
130	C₃×C₄×C₈	—	2	1	no	—
131	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₂×C₂²⋊D₅	—	2	1	no	—
133	C₂²×Dic₅	—	2	1	no	—
134	#709	—	2	1	no	—
135	#709	—	2	1	no	—
136	#709	C₂×C₃×C₄	1	2	yes	—
137	#709	C₂×C₃×C₄	1	2	yes	—
138	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	—	2	1	no	—
140	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
141	C₅×M₁₆	—	2	1	no	—
142	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
145	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
146	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄×Dic₅	—	2	1	no	—
152	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
153	#681	—	2	1	no	—
154	#681	C₂×C₃×C₄	1	2	yes	—
155	C₂×#168	—	2	1	no	—
156	C₂×#168	—	2	1	no	—
157	C₂×#168	—	2	1	no	—
158	C₂×#168	C₂×C₃×C₄	1	2	yes	—
159	#676	—	2	4	no	—
160	C₈×D₅	—	2	4	no	—
161	C₂×#131	—	5	1	no	—
162	C₂×#104	—	5	1	no	—
163	#416	—	5	1	no	—
164	#405	C₃×D₅	1	1	yes	characteristic, complemented
165	C₂×#97	—	5	1	no	—
166	#341	—	5	1	no	—
167	#339	—	5	1	no	—
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	#117	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂×C₃×D₅	—	2	2	no	—
173	C₂×C₃×D₅	—	4	2	no	—
174	C₃×C₄×C₅	—	4	2	no	—
175	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
176	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₃×Dic₅	—	2	2	no	—
180	C₃×Dic₅	—	4	2	no	—
181	C₃×#41	—	5	2	no	—
182	C₃×#41	—	5	2	no	—
183	C₃×#41	—	10	1	no	—
184	C₃×#41	—	10	1	no	—
185	C₂×C₃×Q₈	—	5	1	no	—
186	C₂×C₃×D₄	—	5	1	no	—
187	C₂×C₃×D₄	—	10	1	no	—
188	C₂²×C₃×C₄	—	10	1	no	—
189	C₂²×C₃×C₄	—	10	1	no	—
190	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
191	C₃×M₁₆	—	2	1	no	—
192	C₃×M₁₆	—	5	2	no	—
193	C₃×M₁₆	—	10	1	no	—
194	C₃×M₁₆	—	10	4	no	—
195	C₃×M₁₆	C₄×D₅	1	2	yes	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₂×C₃×C₈	—	5	2	no	—
198	C₂×C₃×C₈	—	10	1	no	—
199	C₂×C₃×C₈	—	10	1	no	—
200	C₂×C₃×C₈	—	10	1	no	—
201	C₂×C₃×C₈	—	10	4	no	—
202	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
203	C₂×C₃×C₈	D₂₀	1	2	yes	—
204	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
205	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
207	C₃×C₂²⋊C₄	—	2	1	no	—
208	C₃×C₄²	—	2	1	no	—
209	C₃×C₄²	—	5	2	no	—
210	C₃×C₄²	—	10	1	no	—
211	C₂³×C₅	C₃×#41	1	1	yes	characteristic
212	C₂²×D₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
220	C₂²⋊D₅	—	2	2	no	—
221	C₂²⋊D₅	—	2	2	no	—
222	C₂×Dic₅	—	2	1	no	—
223	C₂×Dic₅	—	2	2	no	—
224	C₂×Dic₅	—	4	2	no	—
225	D₂₀	—	2	1	no	—
226	D₂₀	C₃×C₄²	1	2	yes	—
227	C₄×D₅	—	2	2	no	—
228	C₄×D₅	—	2	2	no	—
229	Dic₁₀	—	2	1	no	—
230	Dic₁₀	C₃×C₄²	1	2	yes	—
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
233	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
234	#168	—	2	2	no	—
235	#168	—	2	2	no	—
236	C₂×#41	—	5	1	no	—
237	#131	—	5	4	no	—
238	#131	—	10	2	no	—
239	C₂×M₁₆	—	5	1	no	—
240	C₂×M₁₆	—	10	1	no	—
241	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
242	C₂²×C₈	—	5	1	no	—
243	C₂²×C₈	—	10	1	no	—
244	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
245	#117	C₂×C₃×D₅	1	1	yes	characteristic
246	C₂×C₄²	—	5	1	no	—
247	#104	—	5	4	no	—
248	#103	—	5	2	no	—
249	#102	—	5	2	no	—
250	#97	—	2	1	no	—
251	#97	—	10	2	no	—
252	C₄×C₈	—	2	1	no	—
253	C₂×C₃×C₅	—	2	1	no	—
254	C₂×C₃×C₅	—	2	1	no	—
255	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₅	#444	1	2	yes	—
257	C₃×D₅	—	4	2	no	—
258	C₂³×C₃	—	10	1	no	—
259	C₂³×C₃	#709	1	1	yes	characteristic
260	C₃×Q₈	—	5	2	no	—
261	C₃×Q₈	—	10	1	no	—
262	C₃×D₄	—	5	2	no	—
263	C₃×D₄	—	10	2	no	—
264	C₃×D₄	—	10	2	no	—
265	C₃×D₄	—	10	1	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	10	1	no	—
268	C₂×C₃×C₄	—	10	2	no	—
269	C₂×C₃×C₄	—	10	2	no	—
270	C₂×C₃×C₄	—	10	2	no	—
271	C₂×C₃×C₄	—	20	2	no	—
272	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
276	C₂×C₃×C₄	#709	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
278	C₃×C₈	—	2	2	no	—
279	C₃×C₈	—	10	2	no	—
280	C₃×C₈	—	10	2	no	—
281	C₃×C₈	#685	1	2	yes	—
282	C₃×C₈	#685	1	2	yes	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	C₃×#117	1	1	yes	characteristic
285	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
286	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
287	C₂×D₅	—	2	2	no	—
288	C₂×D₅	—	4	2	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
291	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
292	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
293	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
294	Dic₅	—	2	2	no	—
295	Dic₅	—	4	2	no	—
296	#41	—	5	2	no	—
297	#41	—	5	2	no	—
298	#41	—	10	1	no	—
299	#41	—	10	1	no	—
300	C₂×Q₈	—	5	1	no	—
301	C₂×D₄	—	5	1	no	—
302	C₂×D₄	—	10	1	no	—
303	C₂²×C₄	—	10	1	no	—
304	C₂²×C₄	—	10	1	no	—
305	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
306	M₁₆	—	2	1	no	—
307	M₁₆	—	5	2	no	—
308	M₁₆	—	10	1	no	—
309	M₁₆	—	10	4	no	—
310	M₁₆	C₃×C₄×D₅	1	2	yes	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	5	2	no	—
313	C₂×C₈	—	10	1	no	—
314	C₂×C₈	—	10	1	no	—
315	C₂×C₈	—	10	1	no	—
316	C₂×C₈	—	10	4	no	—
317	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
318	C₂×C₈	C₃×D₂₀	1	2	yes	—
319	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
320	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
321	C₄⋊C₄	C₃×C₄×D₅	1	2	yes	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	5	2	no	—
325	C₄²	—	10	1	no	—
326	C₃×C₅	#1765	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	10	2	no	—
329	C₂²×C₃	—	20	2	no	—
330	C₂²×C₃	#4018	1	1	yes	characteristic
331	C₂²×C₃	C₄×D₂₀	1	1	yes	characteristic
332	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
333	C₃×C₄	—	4	2	no	—
334	C₃×C₄	—	10	2	no	—
335	C₃×C₄	—	20	2	no	—
336	C₃×C₄	C₄²×D₅	1	1	yes	characteristic
337	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
338	C₃×C₄	C₂×#685	1	1	yes	characteristic
339	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₅	C₃×#444	1	2	yes	—
344	D₅	—	4	2	no	—
345	C₂³	—	10	1	no	—
346	C₂³	C₃×#709	1	1	yes	characteristic
347	Q₈	—	5	2	no	—
348	Q₈	—	10	1	no	—
349	D₄	—	5	2	no	—
350	D₄	—	10	2	no	—
351	D₄	—	10	2	no	—
352	D₄	—	10	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	10	1	no	—
355	C₂×C₄	—	10	2	no	—
356	C₂×C₄	—	10	2	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	—	20	2	no	—
359	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
361	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
362	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
363	C₂×C₄	C₃×#709	1	1	yes	characteristic
364	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	10	2	no	—
367	C₈	—	10	2	no	—
368	C₈	C₃×#685	1	2	yes	—
369	C₈	C₃×#685	1	2	yes	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	20	2	no	—
373	C₂×C₃	C₄×#685	1	1	yes	characteristic
374	C₂×C₃	#65434	1	2	yes	—
375	C₅	C₃×#1765	1	1	yes	characteristic, complemented, Sylow
376	C₂²	—	2	2	no	—
377	C₂²	—	10	2	no	—
378	C₂²	—	20	2	no	—
379	C₂²	C₃×#4018	1	1	yes	characteristic
380	C₂²	C₃×C₄×D₂₀	1	1	yes	characteristic
381	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
382	C₄	—	4	2	no	—
383	C₄	—	10	2	no	—
384	C₄	—	20	2	no	—
385	C₄	C₃×C₄²×D₅	1	1	yes	characteristic
386	C₄	C₃×C₄×D₂₀	1	1	yes	characteristic
387	C₄	C₂×C₃×#685	1	1	yes	characteristic
388	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
389	C₃	#10600681	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	20	2	no	—
393	C₂	C₃×C₄×#685	1	1	yes	characteristic
394	C₂	C₃×#65434	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#1765
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#405	C₂	semidirect
4. C₂×C₃×#3947	C₂	semidirect
6. C₃×#64778	C₂	semidirect
7. C₃×#64752	C₂	semidirect
8. #10600681	C₃	direct (N × H)
17. C₃×#4047	C₄	semidirect
22. C₃×#3957	C₄	semidirect
24. C₃×#3942	C₄	semidirect
25. C₃×#3941	C₄	semidirect
28. C₅×#405	C₂×C₃	semidirect
30. C₂×#3947	C₂×C₃	semidirect
32. #64778	C₂×C₃	semidirect
33. #64752	C₂×C₃	semidirect
67. C₃×#405	D₅	semidirect
79. #4047	C₃×C₄	semidirect
84. #3957	C₃×C₄	semidirect
86. #3942	C₃×C₄	semidirect
87. #3941	C₃×C₄	semidirect
164. #405	C₃×D₅	semidirect
326. C₃×C₅	#1765	semidirect
375. C₅	C₃×#1765	semidirect
389. C₃	#10600681	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×#4047	2
C₃×C₅×#405	2
C₂×C₃×#3957	2
C₂×C₃×#3947	2
C₃×#65291	2
C₃×#64778	2
C₃×#64752	2
#10600681	3
C₃×#1765	5

Subgroups — C3×#10600681 #14296009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600681 #14296009