Subgroups — #14279894

Order 1920.

1136 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	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#91115	C₂	1	2	yes	maximal
3	C₂×#91115	C₂	1	2	yes	maximal
4	C₂×#91115	C₂	1	2	yes	maximal
5	#10602327	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂³×Dic₁₅	C₂²	1	4	yes	—
10	C₂×C₃×C₄²×C₅	—	2	4	no	—
11	C₂×C₃×C₄²×C₅	C₄	1	4	yes	complemented
12	#91115	—	2	4	no	—
13	#91115	—	2	4	no	—
14	#91115	C₄	1	8	yes	complemented
15	#71534	—	5	1	no	maximal, Hall
16	C₂²×C₄²×C₅	D₃	1	1	yes	characteristic
17	C₂×#3963	—	3	2	no	—
18	C₂×#3963	—	3	2	no	—
19	C₂×#3963	—	3	2	no	—
20	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	—	2	2	no	—
22	C₂²×C₃×C₄×C₅	—	2	2	no	—
23	C₂²×C₃×C₄×C₅	—	2	2	no	—
24	C₂²×C₃×C₄×C₅	—	2	2	no	—
25	C₂²×C₃×C₄×C₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
32	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
34	C₂²×Dic₁₅	—	2	4	no	—
35	C₂²×Dic₁₅	—	2	4	no	—
36	C₂²×Dic₁₅	—	2	4	no	—
37	C₂²×Dic₁₅	—	2	4	no	—
38	C₂²×Dic₁₅	—	2	4	no	—
39	C₂²×Dic₁₅	—	2	4	no	—
40	C₂²×Dic₁₅	C₂×C₄	1	8	yes	—
41	C₃×C₄²×C₅	—	2	8	no	—
42	C₂²×C₃×C₄²	D₅	1	1	yes	characteristic
43	C₂×C₃⋊#95	—	5	2	no	—
44	C₂×C₃⋊#95	—	5	2	no	—
45	C₂×C₃⋊#95	—	5	2	no	—
46	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
47	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
48	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
49	C₂³×Dic₅	—	3	4	no	—
50	C₂×C₄²×C₅	—	2	4	no	—
51	C₂×C₄²×C₅	Dic₃	1	4	yes	complemented
52	#3963	—	3	8	no	—
53	#3963	—	6	4	no	—
54	#3963	—	6	4	no	—
55	#1434	—	15	1	no	Sylow
56	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
57	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
58	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
59	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
60	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
61	C₂³×C₃×C₅	#41	1	2	yes	—
62	C₂³×C₃×C₅	#41	1	2	yes	—
63	C₂³×C₃×C₅	#41	1	2	yes	—
64	C₂³×C₃×C₅	#41	1	2	yes	—
65	C₂×C₃×C₄×C₅	—	2	2	no	—
66	C₂×C₃×C₄×C₅	—	2	2	no	—
67	C₂×C₃×C₄×C₅	—	2	2	no	—
68	C₂×C₃×C₄×C₅	—	2	2	no	—
69	C₂×C₃×C₄×C₅	—	2	2	no	—
70	C₂×C₃×C₄×C₅	—	2	2	no	—
71	C₂×C₃×C₄×C₅	—	2	8	no	—
72	C₂×C₃×C₄×C₅	—	2	4	no	—
73	C₂×C₃×C₄×C₅	—	2	4	no	—
74	C₂×C₃×C₄×C₅	—	2	8	no	—
75	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
76	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
77	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
78	C₂×Dic₁₅	—	2	8	no	—
79	C₂×Dic₁₅	—	2	8	no	—
80	C₂×Dic₁₅	—	2	8	no	—
81	C₂×Dic₁₅	—	4	4	no	—
82	C₂×Dic₁₅	—	4	4	no	—
83	C₂×Dic₁₅	—	4	4	no	—
84	C₂×Dic₁₅	—	4	4	no	—
85	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
86	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
88	C₂³×Dic₃	—	5	4	no	—
89	C₂×C₃×C₄²	—	2	4	no	—
90	C₂×C₃×C₄²	Dic₅	1	4	yes	complemented
91	C₃⋊#95	—	5	8	no	—
92	C₃⋊#95	—	10	4	no	—
93	C₃⋊#95	—	10	4	no	—
94	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	2	no	—
99	C₂²×C₄×C₅	—	2	2	no	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	Dic₆	1	2	yes	—
102	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
103	C₂²×C₄×C₅	D₁₂	1	2	yes	—
104	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
105	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
106	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
107	C₂²×C₄×C₅	#67	1	4	yes	—
108	C₂²×Dic₅	—	3	8	no	—
109	C₂²×Dic₅	—	6	4	no	—
110	C₂²×Dic₅	—	6	4	no	—
111	C₂²×Dic₅	—	6	4	no	—
112	C₂²×Dic₅	—	6	4	no	—
113	C₂²×Dic₅	—	6	4	no	—
114	C₂²×Dic₅	—	6	4	no	—
115	C₄²×C₅	—	2	8	no	—
116	C₂²×C₄²	D₁₅	1	1	yes	characteristic
117	C₂×#95	—	15	2	no	—
118	C₂×#95	—	15	2	no	—
119	C₂×#95	—	15	2	no	—
120	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
121	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₃×C₅	#117	1	4	yes	—
124	C₂²×C₃×C₅	#117	1	1	yes	characteristic
125	C₂²×C₃×C₅	#117	1	1	yes	characteristic
126	C₂²×C₃×C₅	#117	1	1	yes	characteristic
127	C₂²×C₃×C₅	#117	1	1	yes	characteristic
128	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
129	C₂²×C₃×C₅	C₄×D₄	1	4	yes	—
130	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
131	C₂²×C₃×C₅	#121	1	2	yes	—
132	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
133	C₂²×C₃×C₅	#123	1	4	yes	—
134	C₂²×C₃×C₅	#124	1	2	yes	—
135	C₂²×C₃×C₅	#125	1	2	yes	—
136	C₂²×C₃×C₅	#126	1	4	yes	—
137	C₃×C₄×C₅	—	2	4	no	—
138	C₃×C₄×C₅	—	2	4	no	—
139	C₃×C₄×C₅	—	2	4	no	—
140	Dic₁₅	—	4	8	no	—
141	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	2	2	no	—
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	—	2	2	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	—	2	2	no	—
148	C₂²×C₃×C₄	Dic₁₀	1	2	yes	—
149	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
150	C₂²×C₃×C₄	D₂₀	1	2	yes	—
151	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
152	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
153	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
154	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
155	C₂²×Dic₃	—	5	8	no	—
156	C₂²×Dic₃	—	10	4	no	—
157	C₂²×Dic₃	—	10	4	no	—
158	C₂²×Dic₃	—	10	4	no	—
159	C₂²×Dic₃	—	10	4	no	—
160	C₂²×Dic₃	—	10	4	no	—
161	C₂²×Dic₃	—	10	4	no	—
162	C₃×C₄²	—	2	8	no	—
163	C₂³×C₅	C₂×Dic₆	1	1	yes	characteristic
164	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
165	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
166	C₂³×C₅	#235	1	2	yes	—
167	C₂³×C₅	#235	1	2	yes	—
168	C₂³×C₅	#235	1	2	yes	—
169	C₂³×C₅	#235	1	2	yes	—
170	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
171	C₂³×C₅	C₂×#67	1	2	yes	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	8	no	—
178	C₂×C₄×C₅	—	2	8	no	—
179	C₂×C₄×C₅	—	2	4	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
183	C₂×C₄×C₅	C₄⋊Dic₃	1	4	yes	—
184	C₂×C₄×C₅	#217	1	4	yes	—
185	C₂×Dic₅	—	6	8	no	—
186	C₂×Dic₅	—	6	8	no	—
187	C₂×Dic₅	—	6	8	no	—
188	C₂×Dic₅	—	12	4	no	—
189	C₂×Dic₅	—	12	4	no	—
190	C₂×Dic₅	—	12	4	no	—
191	C₂×Dic₅	—	12	4	no	—
192	C₂³×C₄	—	15	4	no	—
193	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
194	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
195	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
196	C₂×C₄²	—	2	4	no	—
197	C₂×C₄²	Dic₁₅	1	4	yes	complemented
198	#95	—	15	8	no	—
199	#95	—	30	4	no	—
200	#95	—	30	4	no	—
201	C₂×C₃×C₅	#376	1	1	yes	characteristic
202	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₃×C₅	#380	1	1	yes	characteristic
205	C₂×C₃×C₅	#381	1	1	yes	characteristic
206	C₂×C₃×C₅	#382	1	1	yes	characteristic
207	C₂×C₃×C₅	#383	1	1	yes	characteristic
208	C₂×C₃×C₅	#387	1	4	yes	—
209	C₂×C₃×C₅	#388	1	4	yes	—
210	C₂³×C₃	C₂×Dic₁₀	1	1	yes	characteristic
211	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
212	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
213	C₂³×C₃	#709	1	2	yes	—
214	C₂³×C₃	#709	1	2	yes	—
215	C₂³×C₃	#709	1	2	yes	—
216	C₂³×C₃	#709	1	2	yes	—
217	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
218	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	4	no	—
222	C₂×C₃×C₄	—	2	2	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	8	no	—
227	C₂×C₃×C₄	—	2	8	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
230	C₂×C₃×C₄	C₄⋊Dic₅	1	4	yes	—
231	C₂×C₃×C₄	C₂²⋊Dic₅	1	4	yes	—
232	C₂×Dic₃	—	10	8	no	—
233	C₂×Dic₃	—	10	8	no	—
234	C₂×Dic₃	—	10	8	no	—
235	C₂×Dic₃	—	20	4	no	—
236	C₂×Dic₃	—	20	4	no	—
237	C₂×Dic₃	—	20	4	no	—
238	C₂×Dic₃	—	20	4	no	—
239	C₂²×C₅	C₄×Dic₆	1	2	yes	—
240	C₂²×C₅	#870	1	2	yes	—
241	C₂²×C₅	#872	1	4	yes	—
242	C₂²×C₅	C₄×D₁₂	1	2	yes	—
243	C₂²×C₅	#875	1	2	yes	—
244	C₂²×C₅	#876	1	4	yes	—
245	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
246	C₂²×C₅	#924	1	2	yes	—
247	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
248	C₂²×C₅	#926	1	1	yes	characteristic
249	C₂²×C₅	#926	1	1	yes	characteristic
250	C₂²×C₅	#926	1	1	yes	characteristic
251	C₂²×C₅	#926	1	1	yes	characteristic
252	C₂²×C₅	C₄×#67	1	4	yes	—
253	C₂²×C₅	#929	1	4	yes	—
254	C₂²×C₅	#930	1	2	yes	—
255	C₂²×C₅	C₂×#217	1	1	yes	characteristic
256	C₄×C₅	—	2	4	no	—
257	C₄×C₅	—	2	4	no	—
258	C₄×C₅	—	2	4	no	—
259	Dic₅	—	12	8	no	—
260	C₂⁴	C₂²×D₁₅	1	1	yes	characteristic
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	15	8	no	—
268	C₂²×C₄	—	30	4	no	—
269	C₂²×C₄	—	30	4	no	—
270	C₂²×C₄	—	30	4	no	—
271	C₂²×C₄	—	30	4	no	—
272	C₂²×C₄	—	30	4	no	—
273	C₂²×C₄	—	30	4	no	—
274	C₂²×C₄	Dic₃₀	1	2	yes	—
275	C₂²×C₄	C₄×D₁₅	1	4	yes	—
276	C₂²×C₄	D₆₀	1	2	yes	—
277	C₂²×C₄	C₂×Dic₁₅	1	2	yes	—
278	C₂²×C₄	C₂×Dic₁₅	1	2	yes	—
279	C₂²×C₄	C₂×Dic₁₅	1	2	yes	—
280	C₂²×C₄	#1220	1	4	yes	—
281	C₄²	—	2	8	no	—
282	C₃×C₅	#1434	1	1	yes	characteristic, complemented, Hall
283	C₂²×C₃	C₄×Dic₁₀	1	2	yes	—
284	C₂²×C₃	#4016	1	2	yes	—
285	C₂²×C₃	#4018	1	4	yes	—
286	C₂²×C₃	C₄×D₂₀	1	2	yes	—
287	C₂²×C₃	#4021	1	2	yes	—
288	C₂²×C₃	#4022	1	4	yes	—
289	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
290	C₂²×C₃	#4070	1	2	yes	—
291	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
292	C₂²×C₃	#4072	1	1	yes	characteristic
293	C₂²×C₃	#4072	1	1	yes	characteristic
294	C₂²×C₃	#4072	1	1	yes	characteristic
295	C₂²×C₃	#4072	1	1	yes	characteristic
296	C₂²×C₃	C₄×C₂²⋊D₅	1	4	yes	—
297	C₂²×C₃	#4075	1	4	yes	—
298	C₂²×C₃	#4076	1	2	yes	—
299	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
300	C₃×C₄	—	2	4	no	—
301	C₃×C₄	—	2	4	no	—
302	C₃×C₄	—	2	4	no	—
303	Dic₃	—	20	8	no	—
304	C₂×C₅	#4932	1	1	yes	characteristic
305	C₂×C₅	#4933	1	4	yes	—
306	C₂×C₅	C₄×C₄⋊Dic₃	1	1	yes	characteristic
307	C₂×C₅	#4936	1	1	yes	characteristic
308	C₂×C₅	#4937	1	1	yes	characteristic
309	C₂×C₅	#4940	1	4	yes	—
310	C₂×C₅	C₄×#217	1	1	yes	characteristic
311	C₂×C₅	#5211	1	1	yes	characteristic
312	C₂×C₅	#5212	1	1	yes	characteristic
313	C₂³	C₂×Dic₃₀	1	1	yes	characteristic
314	C₂³	C₂×C₄×D₁₅	1	2	yes	—
315	C₂³	C₂×D₆₀	1	1	yes	characteristic
316	C₂³	#6817	1	2	yes	—
317	C₂³	#6817	1	2	yes	—
318	C₂³	#6817	1	2	yes	—
319	C₂³	#6817	1	2	yes	—
320	C₂³	C₂²×Dic₁₅	1	1	yes	characteristic
321	C₂³	C₂×#1220	1	2	yes	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	30	8	no	—
333	C₂×C₄	—	30	8	no	—
334	C₂×C₄	—	30	8	no	—
335	C₂×C₄	—	60	4	no	—
336	C₂×C₄	—	60	4	no	—
337	C₂×C₄	—	60	4	no	—
338	C₂×C₄	—	60	4	no	—
339	C₂×C₄	C₄×Dic₁₅	1	4	yes	—
340	C₂×C₄	C₄⋊Dic₁₅	1	4	yes	—
341	C₂×C₄	#6719	1	4	yes	—
342	C₂×C₃	#65221	1	1	yes	characteristic
343	C₂×C₃	#65222	1	4	yes	—
344	C₂×C₃	C₄×C₄⋊Dic₅	1	1	yes	characteristic
345	C₂×C₃	#65225	1	1	yes	characteristic
346	C₂×C₃	#65226	1	1	yes	characteristic
347	C₂×C₃	#65229	1	4	yes	—
348	C₂×C₃	C₄×C₂²⋊Dic₅	1	1	yes	characteristic
349	C₂×C₃	#65500	1	1	yes	characteristic
350	C₂×C₃	#65501	1	1	yes	characteristic
351	C₅	#71534	1	1	yes	characteristic, complemented, Sylow
352	C₂²	C₄×Dic₃₀	1	2	yes	—
353	C₂²	#91759	1	2	yes	—
354	C₂²	#91761	1	4	yes	—
355	C₂²	C₄×D₆₀	1	2	yes	—
356	C₂²	#91764	1	2	yes	—
357	C₂²	#91765	1	4	yes	—
358	C₂²	C₂×C₄×Dic₁₅	1	1	yes	characteristic
359	C₂²	#91813	1	2	yes	—
360	C₂²	C₂×C₄⋊Dic₁₅	1	1	yes	characteristic
361	C₂²	#91815	1	1	yes	characteristic
362	C₂²	#91815	1	1	yes	characteristic
363	C₂²	#91815	1	1	yes	characteristic
364	C₂²	#91815	1	1	yes	characteristic
365	C₂²	C₄×#1220	1	4	yes	—
366	C₂²	#91818	1	4	yes	—
367	C₂²	#91819	1	2	yes	—
368	C₂²	C₂×#6719	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	4	no	—
372	C₄	—	60	8	no	—
373	C₃	#10602327	1	1	yes	characteristic, complemented, Sylow
374	C₂	#11751033	1	1	yes	characteristic
375	C₂	#11751034	1	4	yes	—
376	C₂	C₄×C₄⋊Dic₁₅	1	1	yes	characteristic
377	C₂	#11751037	1	1	yes	characteristic
378	C₂	#11751038	1	1	yes	characteristic
379	C₂	#11751041	1	4	yes	—
380	C₂	C₄×#6719	1	1	yes	characteristic
381	C₂	#11751312	1	1	yes	characteristic
382	C₂	#11751313	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₁₅
commutator	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂²×C₃×C₄²×C₅	C₂
socle, prime radical, cosocle	C₂⁴×C₃×C₅	C₂³
hypercenter	C₂²×C₄²	D₁₅
hypocenter	C₃×C₅	#1434
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
11. C₂×C₃×C₄²×C₅	C₄	semidirect
14. #91115	C₄	semidirect
51. C₂×C₄²×C₅	Dic₃	semidirect
90. C₂×C₃×C₄²	Dic₅	semidirect
197. C₂×C₄²	Dic₁₅	semidirect
282. C₃×C₅	#1434	semidirect
351. C₅	#71534	semidirect
373. C₃	#10602327	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄²×C₅	2
C₂×#91115	2
#10602327	3
#71534	5