Subgroups — #14283204

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 396 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	C₄×C₄⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751027	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746359	C₂	1	2	yes	maximal, complemented
5	#11746358	C₂	1	2	yes	maximal
6	#10602548	—	3	1	no	maximal, Hall
7	C₃×C₅×#126	—	2	1	no	—
8	C₃×C₅×#125	C₄	1	1	yes	characteristic, complemented
9	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
10	C₃×C₅×#123	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#121	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
16	C₃×C₅×#117	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Dic₁₅	—	2	1	no	—
19	C₂×C₄×Dic₁₅	—	2	1	no	—
20	#91115	C₂²	1	2	yes	—
21	#91114	C₂²	1	2	yes	—
22	C₄⋊(C₃⋊#168)	—	2	1	no	—
23	#91087	—	2	1	no	—
24	#71755	—	5	1	no	maximal, Hall
25	C₅×#529	D₃	1	1	yes	characteristic
26	C₄×C₄⋊Dic₅	—	3	1	no	—
27	#65215	—	3	1	no	—
28	#64758	—	3	2	no	—
29	#64757	—	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	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	2	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	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₄⋊Dic₁₅	—	2	4	no	—
55	C₄×Dic₁₅	—	4	2	no	—
56	C₂×C₃⋊#168	—	2	2	no	—
57	C₃×#529	D₅	1	1	yes	characteristic
58	C₄×C₄⋊Dic₃	—	5	1	no	—
59	#4926	—	5	1	no	—
60	#4538	—	5	2	no	—
61	#4537	—	5	2	no	—
62	C₅×#126	—	2	1	no	—
63	C₅×#125	Dic₃	1	1	yes	characteristic, complemented
64	C₅×#124	Dic₃	1	1	yes	characteristic, complemented
65	C₅×#123	—	2	1	no	—
66	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
67	C₅×#121	C₂×D₃	1	1	yes	characteristic
68	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic, complemented
71	C₅×#117	—	2	1	no	—
72	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
73	C₂×C₄⋊Dic₅	—	6	1	no	—
74	C₂×C₄×Dic₅	—	6	1	no	—
75	#3963	—	3	2	no	—
76	C₂²⋊#168	—	3	2	no	—
77	C₄⋊#168	—	6	1	no	—
78	#3935	—	6	1	no	—
79	#1509	—	15	1	no	Sylow
80	C₂³×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	4	1	no	—
83	C₃×C₅×D₄	—	4	1	no	—
84	C₃×C₅×D₄	—	4	1	no	—
85	C₃×C₅×D₄	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	2	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	2	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	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×Dic₁₅	—	2	4	no	—
101	C₂×Dic₁₅	—	4	2	no	—
102	C₂×Dic₁₅	—	4	2	no	—
103	C₃⋊#168	—	4	2	no	—
104	C₃×#126	—	2	1	no	—
105	C₃×#125	Dic₅	1	1	yes	characteristic, complemented
106	C₃×#124	Dic₅	1	1	yes	characteristic, complemented
107	C₃×#123	—	2	1	no	—
108	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
109	C₃×#121	C₂×D₅	1	1	yes	characteristic
110	C₃×C₄×Q₈	Dic₅	1	1	yes	characteristic, complemented
111	C₃×C₄×D₄	—	2	1	no	—
112	C₃×C₄×D₄	Dic₅	1	1	yes	characteristic, complemented
113	C₃×#117	—	2	1	no	—
114	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
115	C₂×C₄⋊Dic₃	—	10	1	no	—
116	C₂×C₄×Dic₃	—	10	1	no	—
117	C₃⋊#95	—	5	2	no	—
118	#830	—	5	2	no	—
119	C₄⋊(C₃⋊C₈)	—	10	1	no	—
120	#803	—	10	1	no	—
121	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	#67	1	1	yes	characteristic
126	C₂²×C₄×C₅	#67	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
128	C₂²×Dic₅	—	6	2	no	—
129	C₅×C₄⋊C₄	—	2	1	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	C₂×Dic₃	1	1	yes	characteristic
134	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
135	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₄²×C₅	—	2	1	no	—
141	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
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	C₄⋊Dic₅	—	6	4	no	—
146	C₄×Dic₅	—	12	2	no	—
147	C₂×#168	—	6	2	no	—
148	#529	D₁₅	1	1	yes	characteristic
149	#432	—	15	1	no	—
150	C₄×C₄⋊C₄	—	15	1	no	—
151	#328	—	15	2	no	—
152	#327	—	15	2	no	—
153	C₂²×C₃×C₅	—	2	1	no	—
154	C₂²×C₃×C₅	—	2	1	no	—
155	C₂²×C₃×C₅	—	4	1	no	—
156	C₂²×C₃×C₅	—	4	1	no	—
157	C₂²×C₃×C₅	—	4	1	no	—
158	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂²×C₃×C₅	#137	1	1	yes	characteristic
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	—	2	1	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	—	4	1	no	—
168	C₃×C₄×C₅	—	4	1	no	—
169	C₃×C₄×C₅	#104	1	2	yes	—
170	Dic₁₅	—	4	4	no	—
171	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
178	C₂²×Dic₃	—	10	2	no	—
179	C₃×C₄⋊C₄	—	2	1	no	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	—	2	1	no	—
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₂²⋊C₄	—	2	1	no	—
188	C₃×C₂²⋊C₄	—	2	1	no	—
189	C₃×C₂²⋊C₄	—	2	1	no	—
190	C₃×C₄²	—	2	1	no	—
191	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
192	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
193	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
194	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
195	C₄⋊Dic₃	—	10	4	no	—
196	C₄×Dic₃	—	20	2	no	—
197	C₂×C₃⋊C₈	—	10	2	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	C₂×#67	1	1	yes	characteristic
200	C₅×Q₈	—	4	1	no	—
201	C₅×D₄	—	4	1	no	—
202	C₅×D₄	—	4	1	no	—
203	C₅×D₄	—	4	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	#217	1	1	yes	characteristic
213	C₂×C₄×C₅	#217	1	1	yes	characteristic
214	C₂×C₄×C₅	#217	1	1	yes	characteristic
215	C₂×C₄×C₅	#217	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
218	C₂×Dic₅	—	6	4	no	—
219	C₂×Dic₅	—	12	2	no	—
220	C₂×Dic₅	—	12	2	no	—
221	#168	—	12	2	no	—
222	#126	—	2	1	no	—
223	#125	Dic₁₅	1	1	yes	characteristic, complemented
224	#124	Dic₁₅	1	1	yes	characteristic, complemented
225	#123	—	2	1	no	—
226	C₂²⋊Q₈	C₂×D₁₅	1	1	yes	characteristic
227	#121	C₂×D₁₅	1	1	yes	characteristic
228	C₄×Q₈	Dic₁₅	1	1	yes	characteristic, complemented
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	Dic₁₅	1	1	yes	characteristic, complemented
231	#117	—	2	1	no	—
232	C₂×C₄⋊C₄	—	30	1	no	—
233	C₂×C₄²	—	30	1	no	—
234	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
235	C₄⋊C₈	—	30	1	no	—
236	C₂²⋊C₈	—	15	2	no	—
237	#97	—	30	1	no	—
238	#95	—	15	2	no	—
239	C₂×C₃×C₅	—	2	1	no	—
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	8	1	no	—
242	C₂×C₃×C₅	#410	1	1	yes	characteristic
243	C₂×C₃×C₅	#417	1	1	yes	characteristic
244	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
247	C₃×Q₈	—	4	1	no	—
248	C₃×D₄	—	4	1	no	—
249	C₃×D₄	—	4	1	no	—
250	C₃×D₄	—	4	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
265	C₂×Dic₃	—	10	4	no	—
266	C₂×Dic₃	—	20	2	no	—
267	C₂×Dic₃	—	20	2	no	—
268	C₃⋊C₈	—	20	2	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	4	1	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	#949	1	1	yes	characteristic
275	C₂²×C₅	#951	1	1	yes	characteristic
276	C₂²×C₅	C₂×#217	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	—	2	1	no	—
282	C₄×C₅	—	4	1	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	4	1	no	—
285	C₄×C₅	#837	1	2	yes	—
286	Dic₅	—	12	4	no	—
287	C₂×Q₈	C₂×Dic₁₅	1	1	yes	characteristic
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂×Dic₁₅	1	1	yes	characteristic
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	30	2	no	—
292	C₂²×C₄	#1220	1	1	yes	characteristic
293	C₂²×C₄	#1220	1	1	yes	characteristic
294	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
295	C₂×C₈	—	30	2	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	30	4	no	—
301	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
302	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	1	no	—
307	C₂²⋊C₄	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	60	2	no	—
310	C₄²	C₂×Dic₁₅	1	1	yes	characteristic
311	C₄²	C₂×Dic₁₅	1	1	yes	characteristic
312	C₄²	#1220	1	1	yes	characteristic
313	C₄²	#1220	1	1	yes	characteristic
314	C₃×C₅	#1509	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	4	1	no	—
318	C₂²×C₃	—	4	1	no	—
319	C₂²×C₃	—	4	1	no	—
320	C₂²×C₃	#4095	1	1	yes	characteristic
321	C₂²×C₃	#4097	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	4	1	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	4	1	no	—
331	C₃×C₄	#3969	1	2	yes	—
332	Dic₃	—	20	4	no	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	2	1	no	—
335	C₂×C₅	—	8	1	no	—
336	C₂×C₅	#5232	1	1	yes	characteristic
337	C₂×C₅	C₂×#837	1	1	yes	characteristic
338	C₂×C₅	#5240	1	1	yes	characteristic
339	C₂³	—	2	1	no	—
340	C₂³	C₂×#1220	1	1	yes	characteristic
341	Q₈	—	4	1	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	1	no	—
344	D₄	—	4	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	30	4	no	—
354	C₂×C₄	—	60	2	no	—
355	C₂×C₄	—	60	2	no	—
356	C₂×C₄	#6719	1	1	yes	characteristic
357	C₂×C₄	#6719	1	1	yes	characteristic
358	C₂×C₄	#6719	1	1	yes	characteristic
359	C₂×C₄	#6719	1	1	yes	characteristic
360	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
361	C₂×C₄	C₂×#1220	1	1	yes	characteristic
362	C₈	—	60	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	8	1	no	—
366	C₂×C₃	#65521	1	1	yes	characteristic
367	C₂×C₃	C₂×#3969	1	1	yes	characteristic
368	C₂×C₃	#65529	1	1	yes	characteristic
369	C₅	#71755	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	#91838	1	1	yes	characteristic
376	C₂²	#91840	1	1	yes	characteristic
377	C₂²	C₂×#6719	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	60	4	no	—
387	C₄	#91121	1	2	yes	—
388	C₃	#10602548	1	1	yes	characteristic, complemented, Sylow
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	8	1	no	—
392	C₂	#11751333	1	1	yes	characteristic
393	C₂	C₂×#91121	1	1	yes	characteristic
394	C₂	#11751341	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#6719
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#529	D₁₅
hypocenter	C₃×C₅	#1509
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #529

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊Dic₁₅	C₂	semidirect
3. #11751027	C₂	semidirect
4. #11746359	C₂	semidirect
8. C₃×C₅×#125	C₄	semidirect
9. C₃×C₅×#124	C₄	semidirect
13. C₃×C₄×C₅×Q₈	C₄	semidirect
15. C₃×C₄×C₅×D₄	C₄	semidirect
63. C₅×#125	Dic₃	semidirect
64. C₅×#124	Dic₃	semidirect
68. C₄×C₅×Q₈	Dic₃	semidirect
70. C₄×C₅×D₄	Dic₃	semidirect
105. C₃×#125	Dic₅	semidirect
106. C₃×#124	Dic₅	semidirect
110. C₃×C₄×Q₈	Dic₅	semidirect
112. C₃×C₄×D₄	Dic₅	semidirect
223. #125	Dic₁₅	semidirect
224. #124	Dic₁₅	semidirect
228. C₄×Q₈	Dic₁₅	semidirect
230. C₄×D₄	Dic₁₅	semidirect
314. C₃×C₅	#1509	semidirect
369. C₅	#71755	semidirect
388. C₃	#10602548	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
C₄×C₄⋊Dic₁₅	2
#11751027	2
#11746359	2
#11746358	2
#10602548	3
#71755	5