Subgroups — C₃×#10610293 #14417633

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4050	C₂	1	1	yes	maximal, characteristic
2	C₃×#65857	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65422	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64999	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×Dic₂₀	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₄₀	C₂	1	2	yes	maximal, complemented
9	#10610293	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
15	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
16	C₃×#4050	C₄	1	8	yes	complemented
17	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
18	C₂×C₃×#677	C₂²	1	2	yes	—
19	C₃×#4038	—	2	2	no	—
20	C₃×D₅×C₄⋊C₄	—	2	2	no	—
21	C₃×#4027	—	2	4	no	—
22	C₃×C₄×D₂₀	C₂²	1	4	yes	—
23	C₃×C₄×Dic₁₀	C₂²	1	4	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₃×#3953	C₂²	1	4	yes	—
27	C₃×#3950	C₂²	1	2	yes	—
28	C₃×#3950	C₂²	1	2	yes	—
29	C₃×#3948	C₂²	1	4	yes	—
30	C₃×#2951	—	5	1	no	maximal, Hall
31	C₂×#4050	C₂×C₃	1	1	yes	characteristic
32	#65857	C₂×C₃	1	2	yes	complemented
33	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
34	#65422	C₂×C₃	1	2	yes	complemented
35	C₂×#3950	C₂×C₃	1	1	yes	characteristic, complemented
36	#64999	C₂×C₃	1	4	yes	complemented
37	C₄×Dic₂₀	C₂×C₃	1	2	yes	complemented
38	C₄×D₄₀	C₂×C₃	1	2	yes	complemented
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
41	C₂²×C₃×Dic₅	—	2	2	no	—
42	C₃×#709	—	2	4	no	—
43	C₃×#709	C₂×C₄	1	8	yes	complemented
44	C₂×C₃×D₂₀	C₂³	1	2	yes	—
45	C₂×C₃×C₄×D₅	—	2	2	no	—
46	C₂×C₃×C₄×D₅	—	2	4	no	—
47	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
48	C₃×C₅×M₁₆	—	2	2	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	C₃×#685	—	2	4	no	—
58	C₃×C₄⋊Dic₅	—	2	2	no	—
59	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
60	C₃×#683	—	2	4	no	—
61	C₃×C₄×Dic₅	—	2	4	no	—
62	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
63	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
64	C₃×#677	C₂×C₄	1	8	yes	complemented
65	C₂×C₃×#135	—	5	1	no	—
66	C₃×#520	—	5	2	no	—
67	C₃×#440	—	5	4	no	—
68	C₃×C₄×Q₁₆	—	5	2	no	—
69	C₃×C₄×D₈	—	5	2	no	—
70	C₂×C₃×#107	—	5	1	no	—
71	C₃×#417	—	5	2	no	—
72	C₃×#405	D₅	1	1	yes	characteristic, complemented
73	C₂×#709	C₂²×C₃	1	2	yes	—
74	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₅×#117	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
78	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
79	#4050	C₃×C₄	1	8	yes	complemented
80	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
81	C₂×#677	C₂²×C₃	1	2	yes	—
82	#4038	—	2	2	no	—
83	D₅×C₄⋊C₄	—	2	2	no	—
84	#4027	—	2	4	no	—
85	C₄×D₂₀	C₂²×C₃	1	4	yes	—
86	C₄×Dic₁₀	C₂²×C₃	1	4	yes	—
87	C₅×#97	C₂²×C₃	1	2	yes	—
88	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
89	#3953	C₂²×C₃	1	4	yes	—
90	#3950	C₂²×C₃	1	2	yes	—
91	#3950	C₂²×C₃	1	2	yes	—
92	#3948	C₂²×C₃	1	4	yes	—
93	#2951	—	5	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₃×D₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
102	C₃×C₂²⋊D₅	—	2	8	no	—
103	C₂×C₃×Dic₅	—	2	2	no	—
104	C₂×C₃×Dic₅	—	2	4	no	—
105	C₂×C₃×Dic₅	—	8	2	no	—
106	C₃×D₂₀	—	2	2	no	—
107	C₃×D₂₀	C₂²×C₄	1	4	yes	—
108	C₃×C₄×D₅	—	2	8	no	—
109	C₃×C₄×D₅	—	8	4	no	—
110	C₃×Dic₁₀	—	2	2	no	—
111	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
112	C₃×C₅×C₈	—	2	2	no	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
115	C₂×C₃×#41	—	5	2	no	—
116	C₃×#135	—	5	8	no	—
117	C₂×C₃×Q₁₆	—	5	1	no	—
118	C₂×C₃×SD₁₆	—	5	2	no	—
119	C₂×C₃×D₈	—	5	1	no	—
120	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
122	C₃×C₄×Q₈	—	5	4	no	—
123	C₃×C₄×D₄	—	5	4	no	—
124	C₃×C₄×D₄	—	10	4	no	—
125	C₃×#117	—	10	2	no	—
126	C₃×#117	C₂×D₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	—	5	2	no	—
128	C₂×C₃×C₄⋊C₄	—	10	2	no	—
129	C₃×#107	—	5	2	no	—
130	C₃×#107	—	5	2	no	—
131	C₃×#103	—	5	4	no	—
132	C₃×#102	—	5	4	no	—
133	C₃×#97	C₂×D₅	1	2	yes	—
134	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₂²⋊D₅	—	2	2	no	—
137	C₂²×Dic₅	—	2	2	no	—
138	#709	—	2	4	no	—
139	#709	C₂×C₃×C₄	1	8	yes	complemented
140	C₂×D₂₀	C₂³×C₃	1	2	yes	—
141	C₂×C₄×D₅	—	2	2	no	—
142	C₂×C₄×D₅	—	2	4	no	—
143	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
144	C₅×M₁₆	—	2	2	no	—
145	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
146	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
147	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
150	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
152	C₄²×C₅	C₂³×C₃	1	2	yes	—
153	#685	—	2	4	no	—
154	C₄⋊Dic₅	—	2	2	no	—
155	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
156	#683	—	2	4	no	—
157	C₄×Dic₅	—	2	4	no	—
158	Dic₂₀	C₂×C₃×C₄	1	4	yes	complemented
159	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
160	#677	C₂×C₃×C₄	1	8	yes	complemented
161	C₂×#135	—	5	1	no	—
162	#520	—	5	2	no	—
163	#440	—	5	4	no	—
164	C₄×Q₁₆	—	5	2	no	—
165	C₄×D₈	—	5	2	no	—
166	C₂×#107	—	5	1	no	—
167	#417	—	5	2	no	—
168	#405	C₃×D₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	1	no	—
170	C₂²×C₃×C₅	—	2	1	no	—
171	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
172	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₃×D₅	—	2	4	no	—
174	C₂×C₃×D₅	—	4	2	no	—
175	C₂×C₃×D₅	—	4	2	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
179	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
181	C₃×Dic₅	—	2	4	no	—
182	C₃×Dic₅	—	4	4	no	—
183	C₃×#41	—	5	8	no	—
184	C₃×#41	—	10	4	no	—
185	C₂×C₃×Q₈	—	5	2	no	—
186	C₂×C₃×D₄	—	5	2	no	—
187	C₂×C₃×D₄	—	10	2	no	—
188	C₂²×C₃×C₄	—	10	2	no	—
189	C₂²×C₃×C₄	—	10	2	no	—
190	C₂²×C₃×C₄	—	10	4	no	—
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
192	C₃×Q₁₆	—	5	4	no	—
193	C₃×SD₁₆	—	5	8	no	—
194	C₃×D₈	—	5	4	no	—
195	C₃×M₁₆	—	2	2	no	—
196	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
197	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
198	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
199	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	5	4	no	—
201	C₃×C₄⋊C₄	—	10	4	no	—
202	C₃×C₄⋊C₄	—	10	2	no	—
203	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
204	C₃×C₄⋊C₄	D₂₀	1	1	yes	characteristic
205	C₃×C₂²⋊C₄	—	10	4	no	—
206	C₃×C₂²⋊C₄	D₂₀	1	2	yes	—
207	C₃×C₄²	—	10	4	no	—
208	C₃×C₄²	C₂²×D₅	1	2	yes	—
209	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
210	C₂²×D₅	—	2	2	no	—
211	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
214	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₃×#41	1	2	yes	—
216	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
217	C₂²⋊D₅	—	2	8	no	—
218	C₂×Dic₅	—	2	2	no	—
219	C₂×Dic₅	—	2	4	no	—
220	C₂×Dic₅	—	8	2	no	—
221	D₂₀	—	2	2	no	—
222	D₂₀	C₂²×C₃×C₄	1	4	yes	—
223	C₄×D₅	—	2	8	no	—
224	C₄×D₅	—	8	4	no	—
225	Dic₁₀	—	2	2	no	—
226	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
229	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
230	C₂×#41	—	5	2	no	—
231	#135	—	5	8	no	—
232	C₂×Q₁₆	—	5	1	no	—
233	C₂×SD₁₆	—	5	2	no	—
234	C₂×D₈	—	5	1	no	—
235	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
236	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
237	C₄×Q₈	—	5	4	no	—
238	C₄×D₄	—	5	4	no	—
239	C₄×D₄	—	10	4	no	—
240	#117	—	10	2	no	—
241	#117	C₂×C₃×D₅	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	5	2	no	—
243	C₂×C₄⋊C₄	—	10	2	no	—
244	#107	—	5	2	no	—
245	#107	—	5	2	no	—
246	#103	—	5	4	no	—
247	#102	—	5	4	no	—
248	#97	C₂×C₃×D₅	1	2	yes	—
249	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
250	C₂×C₃×C₅	—	2	2	no	—
251	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂×C₃×C₅	#576	1	1	yes	characteristic
253	C₂×C₃×C₅	#578	1	1	yes	characteristic
254	C₃×D₅	—	4	4	no	—
255	C₂³×C₃	—	10	2	no	—
256	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
257	C₃×Q₈	—	5	4	no	—
258	C₃×Q₈	—	10	2	no	—
259	C₃×D₄	—	5	4	no	—
260	C₃×D₄	—	10	8	no	—
261	C₃×D₄	—	10	2	no	—
262	C₂×C₃×C₄	—	10	2	no	—
263	C₂×C₃×C₄	—	10	8	no	—
264	C₂×C₃×C₄	—	10	4	no	—
265	C₂×C₃×C₄	—	40	4	no	—
266	C₂×C₃×C₄	—	40	2	no	—
267	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
268	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
269	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
270	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
271	C₂×C₃×C₄	#709	1	2	yes	—
272	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
273	C₃×C₈	—	2	2	no	—
274	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
275	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
279	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
280	C₂×D₅	—	2	4	no	—
281	C₂×D₅	—	4	2	no	—
282	C₂×D₅	—	4	2	no	—
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
286	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
287	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
288	Dic₅	—	2	4	no	—
289	Dic₅	—	4	4	no	—
290	#41	—	5	8	no	—
291	#41	—	10	4	no	—
292	C₂×Q₈	—	5	2	no	—
293	C₂×D₄	—	5	2	no	—
294	C₂×D₄	—	10	2	no	—
295	C₂²×C₄	—	10	2	no	—
296	C₂²×C₄	—	10	2	no	—
297	C₂²×C₄	—	10	4	no	—
298	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
299	Q₁₆	—	5	4	no	—
300	SD₁₆	—	5	8	no	—
301	D₈	—	5	4	no	—
302	M₁₆	—	2	2	no	—
303	C₂×C₈	C₃×C₄×D₅	1	4	yes	complemented
304	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
305	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
306	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
307	C₄⋊C₄	—	5	4	no	—
308	C₄⋊C₄	—	10	2	no	—
309	C₄⋊C₄	—	10	4	no	—
310	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
311	C₄⋊C₄	C₃×D₂₀	1	1	yes	characteristic
312	C₂²⋊C₄	—	10	4	no	—
313	C₂²⋊C₄	C₃×D₂₀	1	2	yes	—
314	C₄²	—	10	4	no	—
315	C₄²	C₂²×C₃×D₅	1	2	yes	—
316	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	10	4	no	—
320	C₂²×C₃	—	20	2	no	—
321	C₂²×C₃	—	20	2	no	—
322	C₂²×C₃	C₄×D₂₀	1	2	yes	—
323	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	10	4	no	—
327	C₃×C₄	—	20	4	no	—
328	C₃×C₄	C₄×D₂₀	1	2	yes	—
329	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
330	C₃×C₄	C₂×#709	1	1	yes	characteristic
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
333	C₂×C₅	C₃×#576	1	1	yes	characteristic
334	C₂×C₅	C₃×#578	1	1	yes	characteristic
335	D₅	—	4	4	no	—
336	C₂³	—	10	2	no	—
337	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
338	Q₈	—	5	4	no	—
339	Q₈	—	10	2	no	—
340	D₄	—	5	4	no	—
341	D₄	—	10	8	no	—
342	D₄	—	10	2	no	—
343	C₂×C₄	—	10	2	no	—
344	C₂×C₄	—	10	8	no	—
345	C₂×C₄	—	10	4	no	—
346	C₂×C₄	—	40	4	no	—
347	C₂×C₄	—	40	2	no	—
348	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
349	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
350	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
351	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
352	C₂×C₄	C₃×#709	1	2	yes	—
353	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
356	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	20	4	no	—
359	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
360	C₂×C₃	#66086	1	1	yes	characteristic
361	C₂×C₃	#66087	1	1	yes	characteristic
362	C₅	C₃×#2951	1	1	yes	characteristic, complemented, Sylow
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	10	4	no	—
366	C₂²	—	20	2	no	—
367	C₂²	—	20	2	no	—
368	C₂²	C₃×C₄×D₂₀	1	2	yes	—
369	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	10	4	no	—
373	C₄	—	20	4	no	—
374	C₄	C₃×C₄×D₂₀	1	2	yes	—
375	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
376	C₄	C₂×C₃×#709	1	1	yes	characteristic
377	C₃	#10610293	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	2	2	no	—
379	C₂	—	20	4	no	—
380	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
381	C₂	C₃×#66086	1	1	yes	characteristic
382	C₂	C₃×#66087	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4050	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#405	D₅
hypocenter	C₅	C₃×#2951
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
2. C₃×#65857	C₂	semidirect
3. C₃×C₅×#405	C₂	semidirect
4. C₃×#65422	C₂	semidirect
5. C₂×C₃×#3950	C₂	semidirect
6. C₃×#64999	C₂	semidirect
7. C₃×C₄×Dic₂₀	C₂	semidirect
8. C₃×C₄×D₄₀	C₂	semidirect
9. #10610293	C₃	direct (N × H)
16. C₃×#4050	C₄	semidirect
32. #65857	C₂×C₃	semidirect
33. C₅×#405	C₂×C₃	semidirect
34. #65422	C₂×C₃	semidirect
35. C₂×#3950	C₂×C₃	semidirect
36. #64999	C₂×C₃	semidirect
37. C₄×Dic₂₀	C₂×C₃	semidirect
38. C₄×D₄₀	C₂×C₃	semidirect
43. C₃×#709	C₂×C₄	semidirect
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. C₃×Dic₂₀	C₂×C₄	semidirect
63. C₃×D₄₀	C₂×C₄	semidirect
64. C₃×#677	C₂×C₄	semidirect
72. C₃×#405	D₅	semidirect
79. #4050	C₃×C₄	semidirect
139. #709	C₂×C₃×C₄	semidirect
145. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
158. Dic₂₀	C₂×C₃×C₄	semidirect
159. D₄₀	C₂×C₃×C₄	semidirect
160. #677	C₂×C₃×C₄	semidirect
168. #405	C₃×D₅	semidirect
196. C₂×C₃×C₈	C₄×D₅	semidirect
303. C₂×C₈	C₃×C₄×D₅	semidirect
316. C₃×C₅	#2951	semidirect
362. C₅	C₃×#2951	semidirect
377. C₃	#10610293	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×#4050	2
C₃×#65857	2
C₃×C₅×#405	2
C₃×#65422	2
C₂×C₃×#3950	2
C₃×#64999	2
C₃×C₄×Dic₂₀	2
C₃×C₄×D₄₀	2
#10610293	3
C₃×#2951	5

Subgroups — C3×#10610293 #14417633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610293 #14417633