Subgroups — C₅×#70798 #14282153

Order 1920.

492 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4484	C₂	1	2	yes	maximal, complemented
5	C₅×#4483	C₂	1	2	yes	maximal, complemented
6	C₅×#1488	—	3	1	no	maximal, Hall
7	C₂×C₅×#235	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₄×C₅×#67	—	2	1	no	—
10	C₄×C₅×#67	—	2	1	no	—
11	C₅×#926	C₄	1	1	yes	characteristic
12	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
13	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
14	C₅×#872	—	2	1	no	—
15	C₄²×C₅×D₃	—	2	1	no	—
16	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
17	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
20	C₃×C₅×#97	—	2	1	no	—
21	C₅×#830	—	2	1	no	—
22	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	#70798	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	—	3	1	no	—
26	C₅×#432	D₃	1	1	yes	characteristic, complemented
27	C₅×#431	—	3	1	no	—
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×#67	—	2	1	no	—
34	C₅×#235	—	2	2	no	—
35	C₅×#235	—	2	2	no	—
36	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₅×#217	—	2	1	no	—
47	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
48	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
49	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₅×Dic₃⋊C₄	—	2	1	no	—
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₄×C₅×Dic₃	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₄×#235	C₂×C₅	1	1	yes	characteristic
58	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
59	#4925	C₂×C₅	1	1	yes	characteristic, complemented
60	#4484	C₂×C₅	1	2	yes	complemented
61	#4483	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×#41	—	3	1	no	—
63	C₄×C₅×Q₈	—	3	1	no	—
64	C₄×C₅×Q₈	—	3	1	no	—
65	C₄×C₅×D₄	—	3	1	no	—
66	C₄×C₅×D₄	—	3	1	no	—
67	C₄×C₅×D₄	—	6	1	no	—
68	C₄×C₅×D₄	—	6	1	no	—
69	C₅×#117	—	3	1	no	—
70	C₅×#117	—	6	1	no	—
71	C₂×C₄²×C₅	—	6	1	no	—
72	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	6	1	no	—
74	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
75	C₅×C₂²⋊C₈	—	2	1	no	—
76	C₅×C₂²⋊C₈	—	6	1	no	—
77	C₅×#97	—	2	1	no	—
78	C₄×C₅×C₈	—	3	2	no	—
79	#1488	—	3	1	no	Sylow
80	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₅×#67	—	2	4	no	—
93	C₂×C₅×Dic₃	—	2	1	no	—
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₅×D₁₂	—	2	1	no	—
97	C₅×D₁₂	M₁₆	1	2	yes	—
98	C₄×C₅×D₃	—	2	4	no	—
99	C₄×C₅×D₃	—	4	2	no	—
100	C₄×C₅×D₃	—	4	2	no	—
101	C₅×Dic₆	—	2	1	no	—
102	C₅×Dic₆	M₁₆	1	2	yes	—
103	C₃×C₅×C₈	—	4	2	no	—
104	C₅×C₃⋊C₈	—	4	2	no	—
105	C₂×#235	C₄×C₅	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
107	C₄×#67	—	2	1	no	—
108	C₄×#67	—	2	1	no	—
109	#926	C₄×C₅	1	1	yes	characteristic
110	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
111	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
112	#872	—	2	1	no	—
113	C₄²×D₃	—	2	1	no	—
114	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
115	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
116	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
117	C₃×C₂²⋊C₈	—	2	1	no	—
118	C₃×#97	—	2	1	no	—
119	#830	—	2	1	no	—
120	C₄⋊(C₃⋊C₈)	—	2	1	no	—
121	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
122	C₅×#41	—	6	2	no	—
123	C₅×#41	—	6	2	no	—
124	C₂×C₅×Q₈	—	3	1	no	—
125	C₂×C₅×D₄	—	3	1	no	—
126	C₂×C₅×D₄	—	6	1	no	—
127	C₂²×C₄×C₅	—	6	1	no	—
128	C₂²×C₄×C₅	—	6	1	no	—
129	C₂²×C₄×C₅	—	6	1	no	—
130	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
132	C₂²×C₄×C₅	#67	1	1	yes	characteristic
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₅×C₄⋊C₄	—	3	1	no	—
136	C₅×C₄⋊C₄	—	3	1	no	—
137	C₅×C₄⋊C₄	—	6	1	no	—
138	C₅×C₄⋊C₄	—	6	1	no	—
139	C₅×C₂²⋊C₄	—	6	1	no	—
140	C₅×C₂²⋊C₄	—	6	1	no	—
141	C₅×C₂²⋊C₄	—	6	1	no	—
142	C₄²×C₅	—	6	1	no	—
143	C₄²×C₅	—	6	1	no	—
144	C₄²×C₅	—	6	1	no	—
145	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
146	C₄²×C₅	D₁₂	1	1	yes	characteristic
147	C₄²×C₅	#67	1	1	yes	characteristic
148	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₄×#41	—	3	1	no	—
150	#432	C₅×D₃	1	1	yes	characteristic, complemented
151	#431	—	3	1	no	—
152	Q₈⋊C₈	—	3	2	no	—
153	D₄⋊C₈	—	3	2	no	—
154	C₂²×C₃×C₅	—	2	1	no	—
155	C₂²×C₃×C₅	—	2	1	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₅×D₃	—	2	2	no	—
159	C₂×C₅×D₃	—	4	1	no	—
160	C₂×C₅×D₃	—	4	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
167	C₃×C₄×C₅	#135	1	2	yes	—
168	C₅×Dic₃	—	2	2	no	—
169	C₅×Dic₃	—	4	1	no	—
170	C₅×Dic₃	—	4	1	no	—
171	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
174	C₂×#67	—	2	1	no	—
175	#235	—	2	2	no	—
176	#235	—	2	2	no	—
177	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
178	C₂×C₄×D₃	—	2	1	no	—
179	C₂×C₄×D₃	—	2	1	no	—
180	C₂×C₄×D₃	—	2	1	no	—
181	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂×C₃×C₈	—	2	2	no	—
183	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
184	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
185	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
186	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
187	#217	—	2	1	no	—
188	(C₂×D₃)⋊C₄	—	2	1	no	—
189	(C₂×D₃)⋊C₄	—	2	1	no	—
190	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
191	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
192	Dic₃⋊C₄	—	2	1	no	—
193	Dic₃⋊C₄	—	2	1	no	—
194	C₄×Dic₃	—	2	1	no	—
195	C₄×Dic₃	—	2	1	no	—
196	C₄×Dic₃	—	2	1	no	—
197	C₂×C₃⋊C₈	—	2	2	no	—
198	C₂³×C₅	—	6	1	no	—
199	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
200	C₅×Q₈	—	3	2	no	—
201	C₅×Q₈	—	6	1	no	—
202	C₅×D₄	—	3	2	no	—
203	C₅×D₄	—	6	4	no	—
204	C₅×D₄	—	6	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	6	4	no	—
210	C₂×C₄×C₅	—	6	1	no	—
211	C₂×C₄×C₅	—	6	1	no	—
212	C₂×C₄×C₅	—	6	1	no	—
213	C₂×C₄×C₅	—	12	2	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₅×C₈	—	4	2	no	—
222	C₅×C₈	—	12	2	no	—
223	C₂×#41	—	3	1	no	—
224	C₄×Q₈	—	3	1	no	—
225	C₄×Q₈	—	3	1	no	—
226	C₄×D₄	—	3	1	no	—
227	C₄×D₄	—	3	1	no	—
228	C₄×D₄	—	6	1	no	—
229	C₄×D₄	—	6	1	no	—
230	#117	—	3	1	no	—
231	#117	—	6	1	no	—
232	C₂×C₄²	—	6	1	no	—
233	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
234	C₄⋊C₈	—	6	1	no	—
235	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
236	C₂²⋊C₈	—	2	1	no	—
237	C₂²⋊C₈	—	6	1	no	—
238	#97	—	2	1	no	—
239	C₄×C₈	—	3	2	no	—
240	C₂×C₃×C₅	—	4	1	no	—
241	C₂×C₃×C₅	#407	1	1	yes	characteristic
242	C₂×C₃×C₅	#416	1	1	yes	characteristic
243	C₂×C₃×C₅	#421	1	1	yes	characteristic
244	C₅×D₃	—	4	2	no	—
245	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×D₃	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	4	1	no	—
251	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	#67	—	2	4	no	—
258	C₂×Dic₃	—	2	1	no	—
259	C₂×Dic₃	—	2	1	no	—
260	C₂×Dic₃	—	2	1	no	—
261	D₁₂	—	2	1	no	—
262	D₁₂	C₅×M₁₆	1	2	yes	—
263	C₄×D₃	—	2	4	no	—
264	C₄×D₃	—	4	2	no	—
265	C₄×D₃	—	4	2	no	—
266	Dic₆	—	2	1	no	—
267	Dic₆	C₅×M₁₆	1	2	yes	—
268	C₃×C₈	—	4	2	no	—
269	C₃⋊C₈	—	4	2	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	6	2	no	—
274	C₂²×C₅	—	12	1	no	—
275	C₂²×C₅	—	12	1	no	—
276	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	6	2	no	—
282	C₄×C₅	—	12	1	no	—
283	C₄×C₅	—	12	1	no	—
284	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
285	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
286	C₄×C₅	#950	1	2	yes	—
287	#41	—	6	2	no	—
288	#41	—	6	2	no	—
289	C₂×Q₈	—	3	1	no	—
290	C₂×D₄	—	3	1	no	—
291	C₂×D₄	—	6	1	no	—
292	C₂²×C₄	—	6	1	no	—
293	C₂²×C₄	—	6	1	no	—
294	C₂²×C₄	—	6	1	no	—
295	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
296	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
297	C₂²×C₄	C₅×#67	1	1	yes	characteristic
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	6	2	no	—
300	C₄⋊C₄	—	3	1	no	—
301	C₄⋊C₄	—	3	1	no	—
302	C₄⋊C₄	—	6	1	no	—
303	C₄⋊C₄	—	6	1	no	—
304	C₂²⋊C₄	—	6	1	no	—
305	C₂²⋊C₄	—	6	1	no	—
306	C₂²⋊C₄	—	6	1	no	—
307	C₄²	—	6	1	no	—
308	C₄²	—	6	1	no	—
309	C₄²	—	6	1	no	—
310	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
311	C₄²	C₅×D₁₂	1	1	yes	characteristic
312	C₄²	C₅×#67	1	1	yes	characteristic
313	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
314	C₃×C₅	#1488	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×D₃	—	2	2	no	—
320	C₂×D₃	—	4	1	no	—
321	C₂×D₃	—	4	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
327	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
328	C₃×C₄	C₅×#135	1	2	yes	—
329	Dic₃	—	2	2	no	—
330	Dic₃	—	4	1	no	—
331	Dic₃	—	4	1	no	—
332	C₂×C₅	—	4	1	no	—
333	C₂×C₅	—	12	2	no	—
334	C₂×C₅	#5002	1	1	yes	characteristic
335	C₂×C₅	#5126	1	1	yes	characteristic
336	C₂×C₅	#5139	1	1	yes	characteristic
337	C₂³	—	6	1	no	—
338	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
339	Q₈	—	3	2	no	—
340	Q₈	—	6	1	no	—
341	D₄	—	3	2	no	—
342	D₄	—	6	4	no	—
343	D₄	—	6	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	6	4	no	—
349	C₂×C₄	—	6	1	no	—
350	C₂×C₄	—	6	1	no	—
351	C₂×C₄	—	6	1	no	—
352	C₂×C₄	—	12	2	no	—
353	C₂×C₄	—	12	2	no	—
354	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
358	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
359	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
360	C₈	—	4	2	no	—
361	C₈	—	12	2	no	—
362	C₂×C₃	—	4	1	no	—
363	C₂×C₃	C₅×#407	1	1	yes	characteristic
364	C₂×C₃	C₅×#416	1	1	yes	characteristic
365	C₂×C₃	C₅×#421	1	1	yes	characteristic
366	D₃	—	4	2	no	—
367	C₅	#70798	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	6	2	no	—
372	C₂²	—	12	1	no	—
373	C₂²	—	12	1	no	—
374	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	6	2	no	—
380	C₄	—	12	1	no	—
381	C₄	—	12	1	no	—
382	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
383	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
384	C₄	C₅×#950	1	2	yes	—
385	C₃	C₅×#1488	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	4	1	no	—
387	C₂	—	12	2	no	—
388	C₂	C₅×#5002	1	1	yes	characteristic
389	C₂	C₅×#5126	1	1	yes	characteristic
390	C₂	C₅×#5139	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×#432	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#432	D₃
hypocenter	C₃	C₅×#1488
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#432

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#432	C₂	semidirect
3. C₅×#4925	C₂	semidirect
4. C₅×#4484	C₂	semidirect
5. C₅×#4483	C₂	semidirect
24. #70798	C₅	direct (N × H)
26. C₅×#432	D₃	semidirect
58. C₃×#432	C₂×C₅	semidirect
59. #4925	C₂×C₅	semidirect
60. #4484	C₂×C₅	semidirect
61. #4483	C₂×C₅	semidirect
150. #432	C₅×D₃	semidirect
314. C₃×C₅	#1488	semidirect
367. C₅	#70798	direct (N × H)
385. C₃	C₅×#1488	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#235	2
C₃×C₅×#432	2
C₅×#4925	2
C₅×#4484	2
C₅×#4483	2
C₅×#1488	3
#70798	5

Subgroups — C5×#70798 #14282153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70798 #14282153