Subgroups — C₅×#71914 #14289220

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5088	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5027	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5015	C₂	1	1	yes	maximal, characteristic
5	C₅×#4547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1627	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
13	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	—	2	1	no	—
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×#215	—	2	1	no	—
18	C₂×C₅×#213	—	2	1	no	—
19	C₅×#874	C₂²	1	1	yes	characteristic
20	C₅×#809	—	2	1	no	—
21	C₅×#809	—	2	1	no	—
22	C₅×#809	—	2	2	no	—
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	#71914	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄×Q₈	D₃	1	1	yes	characteristic, complemented
28	C₅×#486	—	3	1	no	—
29	C₅×#460	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#332	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	4	2	no	—
37	C₂×C₃×C₅×Q₈	—	4	2	no	—
38	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	2	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
51	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₅×#215	—	4	2	no	—
56	C₅×#213	—	4	2	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
61	#5088	C₂×C₅	1	1	yes	characteristic, complemented
62	#5027	C₂×C₅	1	1	yes	characteristic, complemented
63	#5015	C₂×C₅	1	1	yes	characteristic
64	#4547	C₂×C₅	1	1	yes	characteristic, complemented
65	#4535	C₂×C₅	1	1	yes	characteristic, complemented
66	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂²×C₅×Q₈	—	2	1	no	—
68	C₂×C₅×SD₁₆	—	6	1	no	—
69	C₂×C₅×D₈	—	6	1	no	—
70	C₅×C₄⋊Q₈	—	2	1	no	—
71	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
72	C₅×#127	—	3	1	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×C₂²⋊Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	—	3	1	no	—
80	C₅×#102	—	6	1	no	—
81	C₅×#102	—	6	1	no	—
82	C₅×#102	—	6	2	no	—
83	C₄×C₅×C₈	—	3	1	no	—
84	#1627	—	3	1	no	Sylow
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂²×C₅×D₃	—	4	1	no	—
87	C₃×C₅×Q₈	—	2	1	no	—
88	C₃×C₅×Q₈	—	4	4	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₃×C₅×Q₈	—	4	1	no	—
91	C₃×C₅×Q₈	D₈	1	2	yes	complemented
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	SD₁₆	1	2	yes	complemented
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	4	4	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₅×D₁₂	—	4	2	no	—
105	C₅×D₁₂	—	4	1	no	—
106	C₅×D₁₂	—	4	1	no	—
107	C₅×D₁₂	—	4	1	no	—
108	C₅×D₁₂	—	4	1	no	—
109	C₅×C₃⋊C₈	—	4	1	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₅×C₃⋊C₈	—	4	1	no	—
112	C₂²×C₃×Q₈	—	2	1	no	—
113	C₃×C₄⋊Q₈	—	2	1	no	—
114	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
115	C₃×C₂²⋊Q₈	—	2	1	no	—
116	C₃×C₂²⋊Q₈	—	2	2	no	—
117	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
118	C₃×C₄×D₄	—	2	1	no	—
119	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
120	C₂×#215	—	2	1	no	—
121	C₂×#213	—	2	1	no	—
122	#874	C₂²×C₅	1	1	yes	characteristic
123	#809	—	2	1	no	—
124	#809	—	2	1	no	—
125	#809	—	2	2	no	—
126	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
127	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
128	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₅×Q₈	—	2	2	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	—	4	2	no	—
132	C₂×C₅×Q₈	—	4	2	no	—
133	C₂×C₅×Q₈	#67	1	1	yes	characteristic
134	C₂×C₅×D₄	—	6	1	no	—
135	C₂×C₅×D₄	—	6	1	no	—
136	C₂×C₅×D₄	—	6	1	no	—
137	C₂×C₅×D₄	#67	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₅×SD₁₆	—	12	2	no	—
141	C₅×D₈	—	12	2	no	—
142	C₂×C₅×C₈	—	6	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
149	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
150	C₅×C₄⋊C₄	#67	1	2	yes	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
155	D₄×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
156	#486	—	3	1	no	—
157	#460	—	3	1	no	—
158	#459	—	3	1	no	—
159	#332	—	3	1	no	—
160	Q₈⋊C₈	—	3	1	no	—
161	D₄⋊C₈	—	3	1	no	—
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	4	1	no	—
164	C₂²×C₃×C₅	—	4	1	no	—
165	C₂²×C₃×C₅	#120	1	1	yes	characteristic
166	C₂×C₅×D₃	—	8	1	no	—
167	C₂×C₅×D₃	—	8	1	no	—
168	C₂×C₅×D₃	—	8	1	no	—
169	C₃×C₄×C₅	—	2	2	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	1	no	—
173	C₃×C₄×C₅	—	4	1	no	—
174	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
176	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₃×C₄×C₅	#137	1	1	yes	characteristic
178	C₂×C₃×Q₈	—	2	2	no	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	4	2	no	—
181	C₂×C₃×Q₈	—	4	2	no	—
182	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
183	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂×D₁₂	—	2	1	no	—
187	C₂×D₁₂	—	2	1	no	—
188	C₂×D₁₂	—	2	1	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
195	C₃×C₂²⋊C₄	—	2	2	no	—
196	C₃×C₂²⋊C₄	—	2	1	no	—
197	C₃×C₄²	—	2	1	no	—
198	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
199	#215	—	4	2	no	—
200	#213	—	4	2	no	—
201	C₂×C₃⋊C₈	—	2	1	no	—
202	C₂×C₃⋊C₈	—	2	1	no	—
203	C₂×C₃⋊C₈	—	2	1	no	—
204	C₂³×C₅	—	2	1	no	—
205	C₂³×C₅	—	12	1	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	4	4	no	—
208	C₅×Q₈	—	4	1	no	—
209	C₅×Q₈	—	4	1	no	—
210	C₅×Q₈	#213	1	2	yes	complemented
211	C₅×D₄	—	2	1	no	—
212	C₅×D₄	—	12	2	no	—
213	C₅×D₄	—	12	1	no	—
214	C₅×D₄	—	12	1	no	—
215	C₅×D₄	—	12	1	no	—
216	C₅×D₄	—	12	1	no	—
217	C₅×D₄	#215	1	2	yes	complemented
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	4	4	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
228	C₅×C₈	—	12	1	no	—
229	C₅×C₈	—	12	1	no	—
230	C₅×C₈	—	12	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂×SD₁₆	—	6	1	no	—
233	C₂×D₈	—	6	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
236	#127	—	3	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
242	C₄⋊C₈	—	3	1	no	—
243	C₄⋊C₈	—	3	1	no	—
244	#102	—	6	1	no	—
245	#102	—	6	1	no	—
246	#102	—	6	2	no	—
247	C₄×C₈	—	3	1	no	—
248	C₂×C₃×C₅	—	4	2	no	—
249	C₂×C₃×C₅	#447	1	1	yes	characteristic
250	C₂×C₃×C₅	#448	1	1	yes	characteristic
251	C₂×C₃×C₅	#454	1	1	yes	characteristic
252	C₅×D₃	—	16	1	no	—
253	C₂³×C₃	—	2	1	no	—
254	C₂²×D₃	—	4	1	no	—
255	C₃×Q₈	—	2	1	no	—
256	C₃×Q₈	—	4	4	no	—
257	C₃×Q₈	—	4	1	no	—
258	C₃×Q₈	—	4	1	no	—
259	C₃×Q₈	C₅×D₈	1	2	yes	complemented
260	C₃×D₄	—	2	1	no	—
261	C₃×D₄	C₅×SD₁₆	1	2	yes	complemented
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	4	4	no	—
267	C₂×C₃×C₄	—	4	1	no	—
268	C₂×C₃×C₄	—	4	1	no	—
269	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
272	D₁₂	—	4	2	no	—
273	D₁₂	—	4	1	no	—
274	D₁₂	—	4	1	no	—
275	D₁₂	—	4	1	no	—
276	D₁₂	—	4	1	no	—
277	C₃⋊C₈	—	4	1	no	—
278	C₃⋊C₈	—	4	1	no	—
279	C₃⋊C₈	—	4	1	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	4	1	no	—
282	C₂²×C₅	—	4	1	no	—
283	C₂²×C₅	—	24	1	no	—
284	C₂²×C₅	—	24	1	no	—
285	C₂²×C₅	—	24	1	no	—
286	C₂²×C₅	#953	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	4	1	no	—
291	C₄×C₅	—	4	1	no	—
292	C₄×C₅	C₂×#213	1	1	yes	characteristic
293	C₄×C₅	#932	1	1	yes	characteristic
294	C₄×C₅	C₂×#215	1	1	yes	characteristic
295	C₄×C₅	#942	1	1	yes	characteristic
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	C₅×#67	1	1	yes	characteristic
301	C₂×D₄	—	6	1	no	—
302	C₂×D₄	—	6	1	no	—
303	C₂×D₄	—	6	1	no	—
304	C₂×D₄	C₅×#67	1	1	yes	characteristic
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	SD₁₆	—	12	2	no	—
308	D₈	—	12	2	no	—
309	C₂×C₈	—	6	1	no	—
310	C₂×C₈	—	6	1	no	—
311	C₂×C₈	—	6	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
316	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
317	C₄⋊C₄	C₅×#67	1	2	yes	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
322	C₃×C₅	#1627	1	1	yes	characteristic, complemented, Hall
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	4	1	no	—
325	C₂²×C₃	—	4	1	no	—
326	C₂²×C₃	C₅×#120	1	1	yes	characteristic
327	C₂×D₃	—	8	1	no	—
328	C₂×D₃	—	8	1	no	—
329	C₂×D₃	—	8	1	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	4	2	no	—
333	C₃×C₄	—	4	1	no	—
334	C₃×C₄	—	4	1	no	—
335	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
336	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
337	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₃×C₄	C₅×#137	1	1	yes	characteristic
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	—	48	1	no	—
341	C₂×C₅	#5217	1	1	yes	characteristic
342	C₂×C₅	#5227	1	1	yes	characteristic
343	C₂×C₅	#5245	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	12	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	C₅×#213	1	2	yes	complemented
351	D₄	—	2	1	no	—
352	D₄	—	12	2	no	—
353	D₄	—	12	1	no	—
354	D₄	—	12	1	no	—
355	D₄	—	12	1	no	—
356	D₄	—	12	1	no	—
357	D₄	C₅×#215	1	2	yes	complemented
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
366	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
368	C₈	—	12	1	no	—
369	C₈	—	12	1	no	—
370	C₈	—	12	1	no	—
371	C₂×C₃	—	4	2	no	—
372	C₂×C₃	C₅×#447	1	1	yes	characteristic
373	C₂×C₃	C₅×#448	1	1	yes	characteristic
374	C₂×C₃	C₅×#454	1	1	yes	characteristic
375	D₃	—	16	1	no	—
376	C₅	#71914	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	24	1	no	—
381	C₂²	—	24	1	no	—
382	C₂²	—	24	1	no	—
383	C₂²	C₅×#953	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	C₂×C₅×#213	1	1	yes	characteristic
390	C₄	C₅×#932	1	1	yes	characteristic
391	C₄	C₂×C₅×#215	1	1	yes	characteristic
392	C₄	C₅×#942	1	1	yes	characteristic
393	C₃	C₅×#1627	1	1	yes	characteristic, complemented, Sylow
394	C₂	—	4	2	no	—
395	C₂	—	48	1	no	—
396	C₂	C₅×#5217	1	1	yes	characteristic
397	C₂	C₅×#5227	1	1	yes	characteristic
398	C₂	C₅×#5245	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#953
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×D₄×Q₈	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5015	C₂
hypercenter	C₅×D₄×Q₈	D₃
hypocenter	C₃	C₅×#1627
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₄×Q₈	C₂	semidirect
2. C₅×#5088	C₂	semidirect
3. C₅×#5027	C₂	semidirect
5. C₅×#4547	C₂	semidirect
6. C₅×#4535	C₂	semidirect
7. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
26. #71914	C₅	direct (N × H)
27. C₅×D₄×Q₈	D₃	semidirect
60. C₃×D₄×Q₈	C₂×C₅	semidirect
61. #5088	C₂×C₅	semidirect
62. #5027	C₂×C₅	semidirect
64. #4547	C₂×C₅	semidirect
65. #4535	C₂×C₅	semidirect
66. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
91. C₃×C₅×Q₈	D₈	semidirect
93. C₃×C₅×D₄	SD₁₆	semidirect
155. D₄×Q₈	C₅×D₃	semidirect
210. C₅×Q₈	#213	semidirect
217. C₅×D₄	#215	semidirect
259. C₃×Q₈	C₅×D₈	semidirect
261. C₃×D₄	C₅×SD₁₆	semidirect
322. C₃×C₅	#1627	semidirect
350. Q₈	C₅×#213	semidirect
357. D₄	C₅×#215	semidirect
376. C₅	#71914	direct (N × H)
393. C₃	C₅×#1627	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₄×Q₈	2
C₅×#5088	2
C₅×#5027	2
C₅×#5015	2
C₅×#4547	2
C₅×#4535	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1627	3
#71914	5

Subgroups — C5×#71914 #14289220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71914 #14289220