Subgroups — C₅×#78562 #14417632

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×C₅×#904	C₂	1	1	yes	maximal, characteristic
2	C₅×#5523	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5133	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4710	C₂	1	4	yes	maximal, complemented
7	C₄×C₅×Dic₁₂	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×D₂₄	C₂	1	2	yes	maximal, complemented
9	C₅×#2951	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	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×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
15	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
16	C₅×#904	C₄	1	8	yes	complemented
17	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×#204	C₂²	1	2	yes	—
19	C₅×#892	—	2	2	no	—
20	C₅×D₃×C₄⋊C₄	—	2	2	no	—
21	C₅×#67⋊C₄	—	2	4	no	—
22	C₄×C₅×D₁₂	C₂²	1	4	yes	—
23	C₄×C₅×Dic₆	C₂²	1	4	yes	—
24	C₃×C₅×#97	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×#821	C₂²	1	4	yes	—
27	C₅×#818	C₂²	1	2	yes	—
28	C₅×#818	C₂²	1	2	yes	—
29	C₅×#816	C₂²	1	4	yes	—
30	#78562	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₅×#520	—	3	2	no	—
33	C₅×#440	—	3	4	no	—
34	C₄×C₅×Q₁₆	—	3	2	no	—
35	C₄×C₅×D₈	—	3	2	no	—
36	C₂×C₅×#107	—	3	1	no	—
37	C₅×#417	—	3	2	no	—
38	C₅×#405	D₃	1	1	yes	characteristic, complemented
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₅×#67	—	2	2	no	—
41	C₂²×C₅×Dic₃	—	2	2	no	—
42	C₅×#235	—	2	4	no	—
43	C₅×#235	C₂×C₄	1	8	yes	complemented
44	C₂×C₅×D₁₂	C₂³	1	2	yes	—
45	C₂×C₄×C₅×D₃	—	2	2	no	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₅×Dic₆	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	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
58	C₅×C₄⋊Dic₃	—	2	2	no	—
59	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
60	C₅×Dic₃⋊C₄	—	2	4	no	—
61	C₄×C₅×Dic₃	—	2	4	no	—
62	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
63	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
64	C₅×#204	C₂×C₄	1	8	yes	complemented
65	C₂×#904	C₂×C₅	1	1	yes	characteristic
66	#5523	C₂×C₅	1	2	yes	complemented
67	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
68	#5133	C₂×C₅	1	2	yes	complemented
69	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
70	#4710	C₂×C₅	1	4	yes	complemented
71	C₄×Dic₁₂	C₂×C₅	1	2	yes	complemented
72	C₄×D₂₄	C₂×C₅	1	2	yes	complemented
73	C₂×C₅×#41	—	3	2	no	—
74	C₅×#135	—	3	8	no	—
75	C₂×C₅×Q₁₆	—	3	1	no	—
76	C₂×C₅×SD₁₆	—	3	2	no	—
77	C₂×C₅×D₈	—	3	1	no	—
78	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₄×C₅×Q₈	—	3	4	no	—
81	C₄×C₅×D₄	—	3	4	no	—
82	C₄×C₅×D₄	—	6	4	no	—
83	C₅×#117	—	6	2	no	—
84	C₅×#117	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	—	3	2	no	—
86	C₂×C₅×C₄⋊C₄	—	6	2	no	—
87	C₅×#107	—	3	2	no	—
88	C₅×#107	—	3	2	no	—
89	C₅×#103	—	3	4	no	—
90	C₅×#102	—	3	4	no	—
91	C₅×#97	C₂×D₃	1	2	yes	—
92	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
93	#2951	—	3	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₅×D₃	—	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	C₅×#67	—	2	8	no	—
103	C₂×C₅×Dic₃	—	2	2	no	—
104	C₂×C₅×Dic₃	—	2	4	no	—
105	C₂×C₅×Dic₃	—	8	2	no	—
106	C₅×D₁₂	—	2	2	no	—
107	C₅×D₁₂	C₂²×C₄	1	4	yes	—
108	C₄×C₅×D₃	—	2	8	no	—
109	C₄×C₅×D₃	—	8	4	no	—
110	C₅×Dic₆	—	2	2	no	—
111	C₅×Dic₆	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×#235	C₂²×C₅	1	2	yes	—
116	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
118	C₃×#117	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
120	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
121	#904	C₄×C₅	1	8	yes	complemented
122	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
123	C₂×#204	C₂²×C₅	1	2	yes	—
124	#892	—	2	2	no	—
125	D₃×C₄⋊C₄	—	2	2	no	—
126	#67⋊C₄	—	2	4	no	—
127	C₄×D₁₂	C₂²×C₅	1	4	yes	—
128	C₄×Dic₆	C₂²×C₅	1	4	yes	—
129	C₃×#97	C₂²×C₅	1	2	yes	—
130	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
131	#821	C₂²×C₅	1	4	yes	—
132	#818	C₂²×C₅	1	2	yes	—
133	#818	C₂²×C₅	1	2	yes	—
134	#816	C₂²×C₅	1	4	yes	—
135	C₅×#41	—	3	8	no	—
136	C₅×#41	—	6	4	no	—
137	C₂×C₅×Q₈	—	3	2	no	—
138	C₂×C₅×D₄	—	3	2	no	—
139	C₂×C₅×D₄	—	6	2	no	—
140	C₂²×C₄×C₅	—	6	2	no	—
141	C₂²×C₄×C₅	—	6	2	no	—
142	C₂²×C₄×C₅	—	6	4	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×Q₁₆	—	3	4	no	—
145	C₅×SD₁₆	—	3	8	no	—
146	C₅×D₈	—	3	4	no	—
147	C₅×M₁₆	—	2	2	no	—
148	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
149	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
150	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	3	4	no	—
153	C₅×C₄⋊C₄	—	6	2	no	—
154	C₅×C₄⋊C₄	—	6	4	no	—
155	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
156	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	6	4	no	—
158	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
159	C₄²×C₅	—	6	4	no	—
160	C₄²×C₅	C₂²×D₃	1	2	yes	—
161	C₂×#135	—	3	1	no	—
162	#520	—	3	2	no	—
163	#440	—	3	4	no	—
164	C₄×Q₁₆	—	3	2	no	—
165	C₄×D₈	—	3	2	no	—
166	C₂×#107	—	3	1	no	—
167	#417	—	3	2	no	—
168	#405	C₅×D₃	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×C₅×D₃	—	2	4	no	—
174	C₂×C₅×D₃	—	4	2	no	—
175	C₂×C₅×D₃	—	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	C₅×Dic₃	—	2	4	no	—
182	C₅×Dic₃	—	4	4	no	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂×#67	—	2	2	no	—
185	C₂²×Dic₃	—	2	2	no	—
186	#235	—	2	4	no	—
187	#235	C₂×C₄×C₅	1	8	yes	complemented
188	C₂×D₁₂	C₂³×C₅	1	2	yes	—
189	C₂×C₄×D₃	—	2	2	no	—
190	C₂×C₄×D₃	—	2	4	no	—
191	C₂×Dic₆	C₂³×C₅	1	2	yes	—
192	C₃×M₁₆	—	2	2	no	—
193	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
194	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
195	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
196	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
200	C₃×C₄²	C₂³×C₅	1	2	yes	—
201	(C₂×D₃)⋊C₄	—	2	4	no	—
202	C₄⋊Dic₃	—	2	2	no	—
203	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
204	Dic₃⋊C₄	—	2	4	no	—
205	C₄×Dic₃	—	2	4	no	—
206	Dic₁₂	C₂×C₄×C₅	1	4	yes	complemented
207	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
208	#204	C₂×C₄×C₅	1	8	yes	complemented
209	C₂³×C₅	—	6	2	no	—
210	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
211	C₅×Q₈	—	3	4	no	—
212	C₅×Q₈	—	6	2	no	—
213	C₅×D₄	—	3	4	no	—
214	C₅×D₄	—	6	8	no	—
215	C₅×D₄	—	6	2	no	—
216	C₂×C₄×C₅	—	6	2	no	—
217	C₂×C₄×C₅	—	6	8	no	—
218	C₂×C₄×C₅	—	6	4	no	—
219	C₂×C₄×C₅	—	24	4	no	—
220	C₂×C₄×C₅	—	24	2	no	—
221	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
222	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
223	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
224	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
225	C₂×C₄×C₅	#235	1	2	yes	—
226	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
229	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
230	C₂×#41	—	3	2	no	—
231	#135	—	3	8	no	—
232	C₂×Q₁₆	—	3	1	no	—
233	C₂×SD₁₆	—	3	2	no	—
234	C₂×D₈	—	3	1	no	—
235	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
236	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
237	C₄×Q₈	—	3	4	no	—
238	C₄×D₄	—	3	4	no	—
239	C₄×D₄	—	6	4	no	—
240	#117	—	6	2	no	—
241	#117	C₂×C₅×D₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	3	2	no	—
243	C₂×C₄⋊C₄	—	6	2	no	—
244	#107	—	3	2	no	—
245	#107	—	3	2	no	—
246	#103	—	3	4	no	—
247	#102	—	3	4	no	—
248	#97	C₂×C₅×D₃	1	2	yes	—
249	C₄×C₈	C₂×C₅×D₃	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	C₅×D₃	—	4	4	no	—
255	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂²×D₃	—	2	2	no	—
257	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₅×#41	1	2	yes	—
262	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
263	#67	—	2	8	no	—
264	C₂×Dic₃	—	2	2	no	—
265	C₂×Dic₃	—	2	4	no	—
266	C₂×Dic₃	—	8	2	no	—
267	D₁₂	—	2	2	no	—
268	D₁₂	C₂²×C₄×C₅	1	4	yes	—
269	C₄×D₃	—	2	8	no	—
270	C₄×D₃	—	8	4	no	—
271	Dic₆	—	2	2	no	—
272	Dic₆	C₂²×C₄×C₅	1	4	yes	—
273	C₃×C₈	—	2	2	no	—
274	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
275	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	6	4	no	—
279	C₂²×C₅	—	12	2	no	—
280	C₂²×C₅	—	12	2	no	—
281	C₂²×C₅	C₄×D₁₂	1	2	yes	—
282	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	6	4	no	—
286	C₄×C₅	—	12	4	no	—
287	C₄×C₅	C₄×D₁₂	1	2	yes	—
288	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
289	C₄×C₅	C₂×#235	1	1	yes	characteristic
290	#41	—	3	8	no	—
291	#41	—	6	4	no	—
292	C₂×Q₈	—	3	2	no	—
293	C₂×D₄	—	3	2	no	—
294	C₂×D₄	—	6	2	no	—
295	C₂²×C₄	—	6	2	no	—
296	C₂²×C₄	—	6	2	no	—
297	C₂²×C₄	—	6	4	no	—
298	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
299	Q₁₆	—	3	4	no	—
300	SD₁₆	—	3	8	no	—
301	D₈	—	3	4	no	—
302	M₁₆	—	2	2	no	—
303	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
304	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
305	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
306	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
307	C₄⋊C₄	—	3	4	no	—
308	C₄⋊C₄	—	6	2	no	—
309	C₄⋊C₄	—	6	4	no	—
310	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
311	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
312	C₂²⋊C₄	—	6	4	no	—
313	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
314	C₄²	—	6	4	no	—
315	C₄²	C₂²×C₅×D₃	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	C₄×C₅×D₄	1	2	yes	—
320	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
321	C₂×D₃	—	2	4	no	—
322	C₂×D₃	—	4	2	no	—
323	C₂×D₃	—	4	2	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
327	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
328	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
329	Dic₃	—	2	4	no	—
330	Dic₃	—	4	4	no	—
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	12	4	no	—
333	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
334	C₂×C₅	#5752	1	1	yes	characteristic
335	C₂×C₅	#5753	1	1	yes	characteristic
336	C₂³	—	6	2	no	—
337	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
338	Q₈	—	3	4	no	—
339	Q₈	—	6	2	no	—
340	D₄	—	3	4	no	—
341	D₄	—	6	8	no	—
342	D₄	—	6	2	no	—
343	C₂×C₄	—	6	2	no	—
344	C₂×C₄	—	6	8	no	—
345	C₂×C₄	—	6	4	no	—
346	C₂×C₄	—	24	4	no	—
347	C₂×C₄	—	24	2	no	—
348	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
349	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
350	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
351	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
352	C₂×C₄	C₅×#235	1	2	yes	—
353	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
356	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
359	C₂×C₃	C₅×#576	1	1	yes	characteristic
360	C₂×C₃	C₅×#578	1	1	yes	characteristic
361	D₃	—	4	4	no	—
362	C₅	#78562	1	1	yes	characteristic, direct product factor, Sylow
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	6	4	no	—
366	C₂²	—	12	2	no	—
367	C₂²	—	12	2	no	—
368	C₂²	C₄×C₅×D₁₂	1	2	yes	—
369	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	6	4	no	—
373	C₄	—	12	4	no	—
374	C₄	C₄×C₅×D₁₂	1	2	yes	—
375	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
376	C₄	C₂×C₅×#235	1	1	yes	characteristic
377	C₃	C₅×#2951	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	2	2	no	—
379	C₂	—	12	4	no	—
380	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
381	C₂	C₅×#5752	1	1	yes	characteristic
382	C₂	C₅×#5753	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#2951
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
2. C₅×#5523	C₂	semidirect
3. C₃×C₅×#405	C₂	semidirect
4. C₅×#5133	C₂	semidirect
5. C₂×C₅×#818	C₂	semidirect
6. C₅×#4710	C₂	semidirect
7. C₄×C₅×Dic₁₂	C₂	semidirect
8. C₄×C₅×D₂₄	C₂	semidirect
16. C₅×#904	C₄	semidirect
30. #78562	C₅	direct (N × H)
38. C₅×#405	D₃	semidirect
43. C₅×#235	C₂×C₄	semidirect
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. C₅×Dic₁₂	C₂×C₄	semidirect
63. C₅×D₂₄	C₂×C₄	semidirect
64. C₅×#204	C₂×C₄	semidirect
66. #5523	C₂×C₅	semidirect
67. C₃×#405	C₂×C₅	semidirect
68. #5133	C₂×C₅	semidirect
69. C₂×#818	C₂×C₅	semidirect
70. #4710	C₂×C₅	semidirect
71. C₄×Dic₁₂	C₂×C₅	semidirect
72. C₄×D₂₄	C₂×C₅	semidirect
121. #904	C₄×C₅	semidirect
148. C₂×C₅×C₈	C₄×D₃	semidirect
168. #405	C₅×D₃	semidirect
187. #235	C₂×C₄×C₅	semidirect
193. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
206. Dic₁₂	C₂×C₄×C₅	semidirect
207. D₂₄	C₂×C₄×C₅	semidirect
208. #204	C₂×C₄×C₅	semidirect
303. C₂×C₈	C₄×C₅×D₃	semidirect
316. C₃×C₅	#2951	semidirect
362. C₅	#78562	direct (N × H)
377. C₃	C₅×#2951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#904	2
C₅×#5523	2
C₃×C₅×#405	2
C₅×#5133	2
C₂×C₅×#818	2
C₅×#4710	2
C₄×C₅×Dic₁₂	2
C₄×C₅×D₂₄	2
C₅×#2951	3
#78562	5

Subgroups — C5×#78562 #14417632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78562 #14417632