Subgroups — C₃×#10610910 #14413498

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 376 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×#65857	C₂	1	2	yes	maximal
3	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65284	C₂	1	2	yes	maximal, complemented
6	C₃×#65169	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×#107	C₂	1	2	yes	maximal, complemented
8	C₃×#65150	C₂	1	4	yes	maximal, complemented
9	#10610910	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
14	C₂×C₃×#681	C₂²	1	1	yes	characteristic
15	C₃×#4047	C₄	1	8	yes	complemented
16	C₂×C₃×#676	C₂²	1	2	yes	—
17	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
18	C₃×#4038	C₂²	1	4	yes	—
19	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
20	C₃×#4027	—	2	4	no	—
21	C₃×C₄×D₂₀	—	2	2	no	—
22	C₃×C₄×Dic₁₀	—	2	2	no	—
23	C₃×C₅×#107	C₂²	1	1	yes	characteristic
24	C₃×C₅×#107	C₂²	1	1	yes	characteristic
25	C₃×C₅×#106	C₂²	1	2	yes	—
26	C₃×#3950	C₂²	1	2	yes	—
27	C₃×#3950	C₂²	1	2	yes	—
28	C₃×#3940	C₂²	1	4	yes	—
29	C₃×#3939	C₂²	1	4	yes	—
30	C₃×#2913	—	5	1	no	maximal, Hall
31	C₂×#4047	C₂×C₃	1	1	yes	characteristic
32	#65857	C₂×C₃	1	2	yes	—
33	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3950	C₂×C₃	1	1	yes	characteristic, complemented
35	#65284	C₂×C₃	1	2	yes	complemented
36	#65169	C₂×C₃	1	2	yes	complemented
37	D₅×#107	C₂×C₃	1	2	yes	complemented
38	#65150	C₂×C₃	1	4	yes	complemented
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
41	C₂²×C₃×Dic₅	—	2	2	no	—
42	C₃×#709	C₂×C₄	1	4	yes	—
43	C₃×#709	Q₈	1	4	yes	—
44	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	—	2	4	no	—
46	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
47	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
48	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
53	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
54	C₃×C₄²×C₅	—	2	2	no	—
55	C₃×#685	—	2	4	no	—
56	C₃×C₄⋊Dic₅	—	2	2	no	—
57	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
58	C₃×#683	—	2	4	no	—
59	C₃×C₄×Dic₅	—	2	4	no	—
60	C₃×#681	C₂×C₄	1	4	yes	complemented
61	C₂×C₃×#168	C₂³	1	2	yes	—
62	C₃×#676	C₂×C₄	1	8	yes	complemented
63	C₃×C₈×D₅	C₂×C₄	1	8	yes	complemented
64	C₂×C₃×#131	—	5	1	no	—
65	C₃×#520	—	5	2	no	—
66	C₃×#428	—	5	2	no	—
67	C₃×#428	—	5	4	no	—
68	C₃×#427	—	5	2	no	—
69	C₃×#427	D₅	1	1	yes	characteristic, complemented
70	C₂×C₃×#107	—	5	1	no	—
71	C₂×C₃×#107	—	5	2	no	—
72	C₂×#709	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₅×#117	C₂²×C₃	1	2	yes	—
75	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
76	C₂×#681	C₂²×C₃	1	1	yes	characteristic
77	#4047	C₃×C₄	1	8	yes	complemented
78	C₂×#676	C₂²×C₃	1	2	yes	—
79	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
80	#4038	C₂²×C₃	1	4	yes	—
81	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
82	#4027	—	2	4	no	—
83	C₄×D₂₀	—	2	2	no	—
84	C₄×Dic₁₀	—	2	2	no	—
85	C₅×#107	C₂²×C₃	1	1	yes	characteristic
86	C₅×#107	C₂²×C₃	1	1	yes	characteristic
87	C₅×#106	C₂²×C₃	1	2	yes	—
88	#3950	C₂²×C₃	1	2	yes	—
89	#3950	C₂²×C₃	1	2	yes	—
90	#3940	C₂²×C₃	1	4	yes	—
91	#3939	C₂²×C₃	1	4	yes	—
92	#2913	—	5	1	no	Sylow
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₂²⋊D₅	C₄⋊C₄	1	8	yes	—
102	C₂×C₃×Dic₅	—	2	4	no	—
103	C₂×C₃×Dic₅	—	8	2	no	—
104	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
105	C₃×D₂₀	C₄⋊C₄	1	4	yes	—
106	C₃×C₄×D₅	—	8	4	no	—
107	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
108	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
109	C₃×Dic₁₀	C₄⋊C₄	1	4	yes	—
110	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
111	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
112	C₃×#168	C₂²×C₄	1	4	yes	—
113	C₂×C₃×#41	—	5	1	no	—
114	C₃×#131	—	5	8	no	—
115	C₂×C₃×M₁₆	—	5	1	no	—
116	C₂×C₃×M₁₆	—	5	2	no	—
117	C₂²×C₃×C₈	—	5	2	no	—
118	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
119	C₃×C₄×Q₈	—	10	2	no	—
120	C₃×C₄×D₄	—	10	2	no	—
121	C₃×C₄×D₄	—	10	4	no	—
122	C₃×#117	—	5	4	no	—
123	C₃×#117	C₂×D₅	1	2	yes	—
124	C₂×C₃×C₄⋊C₄	—	5	2	no	—
125	C₂×C₃×C₄⋊C₄	—	5	4	no	—
126	C₃×#107	—	5	2	no	—
127	C₃×#107	—	5	2	no	—
128	C₃×#107	—	5	4	no	—
129	C₃×#107	C₂×D₅	1	1	yes	characteristic
130	C₃×#107	C₂×D₅	1	1	yes	characteristic
131	C₃×#106	—	5	4	no	—
132	C₃×#106	C₂×D₅	1	2	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
135	C₂²×Dic₅	—	2	2	no	—
136	#709	C₂×C₃×C₄	1	4	yes	—
137	#709	C₃×Q₈	1	4	yes	—
138	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
139	C₂×C₄×D₅	—	2	4	no	—
140	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
141	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
143	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
146	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
147	C₅×C₂²⋊C₄	—	2	2	no	—
148	C₄²×C₅	—	2	2	no	—
149	#685	—	2	4	no	—
150	C₄⋊Dic₅	—	2	2	no	—
151	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
152	#683	—	2	4	no	—
153	C₄×Dic₅	—	2	4	no	—
154	#681	C₂×C₃×C₄	1	4	yes	complemented
155	C₂×#168	C₂³×C₃	1	2	yes	—
156	#676	C₂×C₃×C₄	1	8	yes	complemented
157	C₈×D₅	C₂×C₃×C₄	1	8	yes	complemented
158	C₂×#131	—	5	1	no	—
159	#520	—	5	2	no	—
160	#428	—	5	2	no	—
161	#428	—	5	4	no	—
162	#427	—	5	2	no	—
163	#427	C₃×D₅	1	1	yes	characteristic, complemented
164	C₂×#107	—	5	1	no	—
165	C₂×#107	—	5	2	no	—
166	C₂²×C₃×C₅	—	2	1	no	—
167	C₂²×C₃×C₅	—	2	1	no	—
168	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
169	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₃×D₅	—	2	2	no	—
171	C₂×C₃×D₅	—	2	2	no	—
172	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	—	4	2	no	—
175	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
176	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
178	C₃×Dic₅	—	4	4	no	—
179	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
180	C₃×#41	—	5	4	no	—
181	C₃×#41	—	5	4	no	—
182	C₂×C₃×Q₈	—	5	1	no	—
183	C₂×C₃×D₄	—	5	2	no	—
184	C₂×C₃×D₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	2	no	—
186	C₂²×C₃×C₄	—	10	4	no	—
187	C₂²×C₃×C₄	—	10	2	no	—
188	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
189	C₃×M₁₆	—	5	4	no	—
190	C₃×M₁₆	—	5	8	no	—
191	C₂×C₃×C₈	—	5	2	no	—
192	C₂×C₃×C₈	—	5	8	no	—
193	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
194	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
195	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
196	C₃×C₄⋊C₄	—	5	4	no	—
197	C₃×C₄⋊C₄	—	10	4	no	—
198	C₃×C₄⋊C₄	—	10	2	no	—
199	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
200	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	—	10	4	no	—
203	C₃×C₄²	—	2	2	no	—
204	C₃×C₄²	—	10	4	no	—
205	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
212	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
213	C₂²⋊D₅	C₃×C₄⋊C₄	1	8	yes	—
214	C₂×Dic₅	—	2	4	no	—
215	C₂×Dic₅	—	8	2	no	—
216	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
217	D₂₀	C₃×C₄⋊C₄	1	4	yes	—
218	C₄×D₅	—	8	4	no	—
219	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
220	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
221	Dic₁₀	C₃×C₄⋊C₄	1	4	yes	—
222	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
223	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
224	#168	C₂²×C₃×C₄	1	4	yes	—
225	C₂×#41	—	5	1	no	—
226	#131	—	5	8	no	—
227	C₂×M₁₆	—	5	1	no	—
228	C₂×M₁₆	—	5	2	no	—
229	C₂²×C₈	—	5	2	no	—
230	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
231	C₄×Q₈	—	10	2	no	—
232	C₄×D₄	—	10	2	no	—
233	C₄×D₄	—	10	4	no	—
234	#117	—	5	4	no	—
235	#117	C₂×C₃×D₅	1	2	yes	—
236	C₂×C₄⋊C₄	—	5	2	no	—
237	C₂×C₄⋊C₄	—	5	4	no	—
238	#107	—	5	2	no	—
239	#107	—	5	2	no	—
240	#107	—	5	4	no	—
241	#107	C₂×C₃×D₅	1	1	yes	characteristic
242	#107	C₂×C₃×D₅	1	1	yes	characteristic
243	#106	—	5	4	no	—
244	#106	C₂×C₃×D₅	1	2	yes	—
245	C₂×C₃×C₅	—	2	2	no	—
246	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₅	#576	1	1	yes	characteristic
248	C₂×C₃×C₅	#578	1	1	yes	characteristic
249	C₃×D₅	—	2	4	no	—
250	C₂³×C₃	—	5	2	no	—
251	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
252	C₃×Q₈	—	5	4	no	—
253	C₃×D₄	—	5	8	no	—
254	C₃×D₄	—	5	4	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	5	2	no	—
258	C₂×C₃×C₄	—	5	4	no	—
259	C₂×C₃×C₄	—	5	4	no	—
260	C₂×C₃×C₄	—	10	4	no	—
261	C₂×C₃×C₄	—	40	4	no	—
262	C₂×C₃×C₄	—	40	2	no	—
263	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
264	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
265	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
266	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
267	C₃×C₈	—	5	4	no	—
268	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
269	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
273	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
274	C₂×D₅	—	2	2	no	—
275	C₂×D₅	—	2	2	no	—
276	C₂×D₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
280	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
281	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
282	Dic₅	—	4	4	no	—
283	Dic₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
284	#41	—	5	4	no	—
285	#41	—	5	4	no	—
286	C₂×Q₈	—	5	1	no	—
287	C₂×D₄	—	5	2	no	—
288	C₂×D₄	—	5	1	no	—
289	C₂²×C₄	—	5	2	no	—
290	C₂²×C₄	—	10	4	no	—
291	C₂²×C₄	—	10	2	no	—
292	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
293	M₁₆	—	5	4	no	—
294	M₁₆	—	5	8	no	—
295	C₂×C₈	—	5	2	no	—
296	C₂×C₈	—	5	8	no	—
297	C₂×C₈	C₃×C₄×D₅	1	4	yes	complemented
298	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
299	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
300	C₄⋊C₄	—	5	4	no	—
301	C₄⋊C₄	—	10	4	no	—
302	C₄⋊C₄	—	10	2	no	—
303	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
304	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	10	4	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	10	4	no	—
309	C₃×C₅	#2913	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	5	4	no	—
313	C₂²×C₃	—	10	2	no	—
314	C₂²×C₃	—	10	2	no	—
315	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
316	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	2	no	—
319	C₃×C₄	—	5	4	no	—
320	C₃×C₄	—	20	4	no	—
321	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
322	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
323	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₅	C₃×#576	1	1	yes	characteristic
327	C₂×C₅	C₃×#578	1	1	yes	characteristic
328	D₅	—	2	4	no	—
329	C₂³	—	5	2	no	—
330	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
331	Q₈	—	5	4	no	—
332	D₄	—	5	8	no	—
333	D₄	—	5	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	5	2	no	—
337	C₂×C₄	—	5	4	no	—
338	C₂×C₄	—	5	4	no	—
339	C₂×C₄	—	10	4	no	—
340	C₂×C₄	—	40	4	no	—
341	C₂×C₄	—	40	2	no	—
342	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
343	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
344	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
345	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
346	C₈	—	5	4	no	—
347	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
348	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	10	4	no	—
351	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
352	C₂×C₃	#66103	1	1	yes	characteristic
353	C₂×C₃	#66105	1	1	yes	characteristic
354	C₅	C₃×#2913	1	1	yes	characteristic, complemented, Sylow
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	5	4	no	—
358	C₂²	—	10	2	no	—
359	C₂²	—	10	2	no	—
360	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
361	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	5	4	no	—
365	C₄	—	20	4	no	—
366	C₄	C₃×D₅×C₄⋊C₄	1	2	yes	—
367	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
368	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
369	C₃	#10610910	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	2	no	—
371	C₂	—	10	4	no	—
372	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
373	C₂	C₃×#66103	1	1	yes	characteristic
374	C₂	C₃×#66105	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#427	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#427	D₅
hypocenter	C₅	C₃×#2913
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#427

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#427	C₂	semidirect
4. C₂×C₃×#3950	C₂	semidirect
5. C₃×#65284	C₂	semidirect
6. C₃×#65169	C₂	semidirect
7. C₃×D₅×#107	C₂	semidirect
8. C₃×#65150	C₂	semidirect
9. #10610910	C₃	direct (N × H)
15. C₃×#4047	C₄	semidirect
33. C₅×#427	C₂×C₃	semidirect
34. C₂×#3950	C₂×C₃	semidirect
35. #65284	C₂×C₃	semidirect
36. #65169	C₂×C₃	semidirect
37. D₅×#107	C₂×C₃	semidirect
38. #65150	C₂×C₃	semidirect
48. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
60. C₃×#681	C₂×C₄	semidirect
62. C₃×#676	C₂×C₄	semidirect
63. C₃×C₈×D₅	C₂×C₄	semidirect
69. C₃×#427	D₅	semidirect
77. #4047	C₃×C₄	semidirect
142. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
154. #681	C₂×C₃×C₄	semidirect
156. #676	C₂×C₃×C₄	semidirect
157. C₈×D₅	C₂×C₃×C₄	semidirect
163. #427	C₃×D₅	semidirect
193. C₂×C₃×C₈	C₄×D₅	semidirect
297. C₂×C₈	C₃×C₄×D₅	semidirect
309. C₃×C₅	#2913	semidirect
354. C₅	C₃×#2913	semidirect
369. C₃	#10610910	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×#65857	2
C₃×C₅×#427	2
C₂×C₃×#3950	2
C₃×#65284	2
C₃×#65169	2
C₃×D₅×#107	2
C₃×#65150	2
#10610910	3
C₃×#2913	5

Subgroups — C3×#10610910 #14413498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610910 #14413498