Subgroups — C₅×#71751 #14281924

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4535	C₂	1	2	yes	maximal, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
6	C₅×#1483	—	3	1	no	maximal, Hall
7	C₃×C₅×#126	—	2	1	no	—
8	C₃×C₅×#125	C₄	1	1	yes	characteristic
9	C₃×C₅×#124	C₄	1	1	yes	characteristic
10	C₃×C₅×#123	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
12	C₃×C₅×#121	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	—	2	1	no	—
19	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
20	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
22	C₅×#803	—	2	1	no	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	#71751	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#529	D₃	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	—	3	1	no	—
27	C₄×C₅×M₁₆	—	3	1	no	—
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₄	—	2	1	no	—
38	C₃×C₅×C₄⋊C₄	—	2	1	no	—
39	C₃×C₅×C₄⋊C₄	—	2	1	no	—
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×#208	—	2	4	no	—
54	C₂×C₅×C₃⋊C₈	—	2	2	no	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	4	2	no	—
57	C₃×#529	C₂×C₅	1	1	yes	characteristic
58	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
59	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
60	#4535	C₂×C₅	1	2	yes	complemented
61	D₄⋊(C₃⋊C₈)	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×M₁₆	—	6	1	no	—
63	C₂²×C₅×C₈	—	6	1	no	—
64	C₅×#126	—	2	1	no	—
65	C₅×#125	Dic₃	1	1	yes	characteristic
66	C₅×#124	Dic₃	1	1	yes	characteristic
67	C₅×#123	—	2	1	no	—
68	C₅×C₂²⋊Q₈	Dic₃	1	1	yes	characteristic
69	C₅×#121	Dic₃	1	1	yes	characteristic
70	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
73	C₅×#117	—	2	1	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	3	2	no	—
76	C₅×C₄⋊C₈	—	6	1	no	—
77	C₅×#97	—	6	1	no	—
78	C₄×C₅×C₈	—	3	2	no	—
79	#1483	—	3	1	no	Sylow
80	C₂³×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	2	no	—
83	C₃×C₅×D₄	—	2	2	no	—
84	C₃×C₅×D₄	—	4	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₅×C₃⋊C₈	—	2	4	no	—
101	C₅×C₃⋊C₈	—	4	2	no	—
102	C₃×#126	—	2	1	no	—
103	C₃×#125	C₄×C₅	1	1	yes	characteristic
104	C₃×#124	C₄×C₅	1	1	yes	characteristic
105	C₃×#123	—	2	1	no	—
106	C₃×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
107	C₃×#121	C₄×C₅	1	1	yes	characteristic
108	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
109	C₃×C₄×D₄	—	2	1	no	—
110	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
111	C₃×#117	—	2	1	no	—
112	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
113	C₂×#208	—	2	1	no	—
114	C₂²×C₃⋊C₈	—	2	1	no	—
115	C₄⋊(C₃⋊C₈)	—	2	1	no	—
116	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
117	#803	—	2	1	no	—
118	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
119	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	#67	1	1	yes	characteristic
125	C₂²×C₄×C₅	#67	1	1	yes	characteristic
126	C₅×M₁₆	—	6	4	no	—
127	C₂×C₅×C₈	—	6	2	no	—
128	C₂×C₅×C₈	—	6	2	no	—
129	C₂×C₅×C₈	—	12	2	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
135	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
136	C₅×C₂²⋊C₄	—	2	1	no	—
137	C₅×C₂²⋊C₄	—	2	1	no	—
138	C₅×C₂²⋊C₄	—	2	1	no	—
139	C₅×C₂²⋊C₄	—	2	1	no	—
140	C₅×C₂²⋊C₄	—	2	1	no	—
141	C₄²×C₅	—	2	1	no	—
142	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
143	C₄²×C₅	#67	1	1	yes	characteristic
144	C₄²×C₅	#67	1	1	yes	characteristic
145	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
146	#529	C₅×D₃	1	1	yes	characteristic
147	C₂×C₄⋊C₈	—	3	1	no	—
148	C₄×M₁₆	—	3	1	no	—
149	Q₈⋊C₈	—	3	2	no	—
150	D₄⋊C₈	—	3	2	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	—	2	1	no	—
153	C₂²×C₃×C₅	—	4	1	no	—
154	C₂²×C₃×C₅	—	4	1	no	—
155	C₂²×C₃×C₅	—	4	1	no	—
156	C₂²×C₃×C₅	#104	1	2	yes	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	4	1	no	—
163	C₃×C₄×C₅	—	4	1	no	—
164	C₃×C₄×C₅	—	4	1	no	—
165	C₃×C₄×C₅	#131	1	2	yes	—
166	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₃×C₄×C₅	#137	1	1	yes	characteristic
168	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	1	no	—
170	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	1	no	—
179	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
180	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
181	C₃×C₂²⋊C₄	—	2	1	no	—
182	C₃×C₂²⋊C₄	—	2	1	no	—
183	C₃×C₂²⋊C₄	—	2	1	no	—
184	C₃×C₂²⋊C₄	—	2	1	no	—
185	C₃×C₂²⋊C₄	—	2	1	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
188	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
189	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
190	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
191	#208	—	2	4	no	—
192	C₂×C₃⋊C₈	—	2	2	no	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	C₂×C₃⋊C₈	—	4	2	no	—
195	C₂³×C₅	—	2	1	no	—
196	C₂³×C₅	#217	1	1	yes	characteristic
197	C₅×Q₈	—	2	2	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	4	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	#217	1	1	yes	characteristic
210	C₂×C₄×C₅	#217	1	1	yes	characteristic
211	C₂×C₄×C₅	#217	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
215	C₅×C₈	—	6	4	no	—
216	C₅×C₈	—	12	2	no	—
217	C₂×M₁₆	—	6	1	no	—
218	C₂²×C₈	—	6	1	no	—
219	#126	—	2	1	no	—
220	#125	C₅×Dic₃	1	1	yes	characteristic
221	#124	C₅×Dic₃	1	1	yes	characteristic
222	#123	—	2	1	no	—
223	C₂²⋊Q₈	C₅×Dic₃	1	1	yes	characteristic
224	#121	C₅×Dic₃	1	1	yes	characteristic
225	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
228	#117	—	2	1	no	—
229	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
230	C₄⋊C₈	—	3	2	no	—
231	C₄⋊C₈	—	6	1	no	—
232	#97	—	6	1	no	—
233	C₄×C₈	—	3	2	no	—
234	C₂×C₃×C₅	—	2	2	no	—
235	C₂×C₃×C₅	—	8	1	no	—
236	C₂×C₃×C₅	#408	1	1	yes	characteristic
237	C₂×C₃×C₅	#417	1	1	yes	characteristic
238	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
239	C₂³×C₃	—	2	1	no	—
240	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
241	C₃×Q₈	—	2	2	no	—
242	C₃×D₄	—	2	2	no	—
243	C₃×D₄	—	4	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	4	1	no	—
252	C₂×C₃×C₄	—	4	1	no	—
253	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₃⋊C₈	—	2	4	no	—
260	C₃⋊C₈	—	4	2	no	—
261	C₂²×C₅	—	2	1	no	—
262	C₂²×C₅	—	2	1	no	—
263	C₂²×C₅	—	4	1	no	—
264	C₂²×C₅	—	4	1	no	—
265	C₂²×C₅	—	4	1	no	—
266	C₂²×C₅	#837	1	2	yes	—
267	C₂²×C₅	C₂×#217	1	1	yes	characteristic
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	4	1	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	4	1	no	—
275	C₄×C₅	#948	1	2	yes	—
276	C₄×C₅	#949	1	1	yes	characteristic
277	C₄×C₅	#951	1	1	yes	characteristic
278	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
283	C₂²×C₄	C₅×#67	1	1	yes	characteristic
284	C₂²×C₄	C₅×#67	1	1	yes	characteristic
285	M₁₆	—	6	4	no	—
286	C₂×C₈	—	6	2	no	—
287	C₂×C₈	—	6	2	no	—
288	C₂×C₈	—	12	2	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
294	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
295	C₂²⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	—	2	1	no	—
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	2	1	no	—
299	C₂²⋊C₄	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
302	C₄²	C₅×#67	1	1	yes	characteristic
303	C₄²	C₅×#67	1	1	yes	characteristic
304	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
305	C₃×C₅	#1483	1	1	yes	characteristic, complemented, Hall
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	4	1	no	—
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	4	1	no	—
311	C₂²×C₃	C₅×#104	1	2	yes	—
312	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	4	1	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	C₅×#131	1	2	yes	—
321	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₃×C₄	C₅×#137	1	1	yes	characteristic
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	8	1	no	—
325	C₂×C₅	#5232	1	1	yes	characteristic
326	C₂×C₅	#5234	1	1	yes	characteristic
327	C₂×C₅	C₂×#837	1	1	yes	characteristic
328	C₂³	—	2	1	no	—
329	C₂³	C₅×#217	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	D₄	—	2	2	no	—
332	D₄	—	4	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	C₅×#217	1	1	yes	characteristic
343	C₂×C₄	C₅×#217	1	1	yes	characteristic
344	C₂×C₄	C₅×#217	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
348	C₈	—	6	4	no	—
349	C₈	—	12	2	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	8	1	no	—
352	C₂×C₃	C₅×#408	1	1	yes	characteristic
353	C₂×C₃	C₅×#417	1	1	yes	characteristic
354	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
355	C₅	#71751	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	C₅×#837	1	2	yes	—
362	C₂²	C₂×C₅×#217	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	C₅×#948	1	2	yes	—
371	C₄	C₅×#949	1	1	yes	characteristic
372	C₄	C₅×#951	1	1	yes	characteristic
373	C₃	C₅×#1483	1	1	yes	characteristic, complemented, Sylow
374	C₂	—	2	2	no	—
375	C₂	—	8	1	no	—
376	C₂	C₅×#5232	1	1	yes	characteristic
377	C₂	C₅×#5234	1	1	yes	characteristic
378	C₂	C₂×C₅×#837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#529	D₃
hypocenter	C₃	C₅×#1483
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#529

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
3. C₄×C₅×#208	C₂	semidirect
4. C₅×#4535	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
24. #71751	C₅	direct (N × H)
58. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
59. C₄×#208	C₂×C₅	semidirect
60. #4535	C₂×C₅	semidirect
61. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
305. C₃×C₅	#1483	semidirect
355. C₅	#71751	direct (N × H)
373. C₃	C₅×#1483	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#529	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₄×C₅×#208	2
C₅×#4535	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1483	3
#71751	5

Subgroups — C5×#71751 #14281924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71751 #14281924