Subgroups — C₅×#73849 #14322380

Order 1920.

2320 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	C₂³×C₅×#67	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4956	C₂	1	8	yes	maximal, complemented
6	C₅×#4943	C₂	1	2	yes	maximal, complemented
7	C₅×#2308	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	—	2	8	no	—
11	C₂²×C₅×#67	C₄	1	8	yes	complemented
12	C₂²×C₅×#67	C₂²	1	4	yes	—
13	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₅×#217	C₂²	1	2	yes	—
18	C₂×C₅×#217	C₂²	1	4	yes	complemented
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
20	C₅×D₃×C₂²⋊C₄	—	2	8	no	—
21	C₅×C₃⋊#95	C₂²	1	8	yes	complemented
22	#73849	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂³×C₅×D₄	—	3	1	no	—
24	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
25	C₅×#386	—	3	8	no	—
26	C₅×#381	—	3	2	no	—
27	C₅×#379	—	3	1	no	—
28	C₅×#379	D₃	1	1	yes	characteristic, complemented
29	C₂⁴×C₃×C₅	—	2	4	no	—
30	C₂⁴×C₃×C₅	—	4	4	no	—
31	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
32	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂³×C₅×D₃	—	4	4	no	—
35	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
36	C₂³×C₅×D₃	D₄	1	8	yes	—
37	C₂³×C₅×D₃	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂×C₅×#67	—	2	32	no	—
40	C₂×C₅×#67	—	2	8	no	—
41	C₂×C₅×#67	—	2	8	no	—
42	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
43	C₂²×C₅×Dic₃	—	2	4	no	—
44	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
45	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
46	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
47	C₂×C₄×C₅×D₃	—	2	8	no	—
48	C₂×C₄×C₅×D₃	—	4	8	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
50	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
51	C₅×#217	—	2	4	no	—
52	C₅×#217	—	4	4	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
54	C₂³×#67	C₂×C₅	1	1	yes	characteristic
55	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
56	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
57	#5247	C₂×C₅	1	1	yes	characteristic, complemented
58	#4956	C₂×C₅	1	8	yes	complemented
59	#4943	C₂×C₅	1	2	yes	complemented
60	C₂⁵×C₅	—	3	1	no	—
61	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₅×D₄	—	3	8	no	—
63	C₂²×C₅×D₄	—	3	4	no	—
64	C₂²×C₅×D₄	—	6	8	no	—
65	C₂³×C₄×C₅	—	3	1	no	—
66	C₂³×C₄×C₅	—	3	4	no	—
67	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
68	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
69	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
70	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
71	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
73	C₅×#95	—	3	8	no	—
74	#2308	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	2	8	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	—	4	8	no	—
81	C₂³×C₃×C₅	—	4	16	no	—
82	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
83	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₂²×C₅×D₃	—	2	8	no	—
87	C₂²×C₅×D₃	—	4	8	no	—
88	C₂²×C₅×D₃	—	4	16	no	—
89	C₂²×C₅×D₃	C₂²⋊C₄	1	16	yes	complemented
90	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
92	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	8	no	—
95	C₅×#67	—	2	32	no	—
96	C₂×C₅×Dic₃	—	2	8	no	—
97	C₂×C₅×Dic₃	—	2	4	no	—
98	C₂×C₅×Dic₃	—	2	4	no	—
99	C₂×C₅×Dic₃	—	2	8	no	—
100	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
101	C₄×C₅×D₃	—	4	16	no	—
102	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
103	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
104	C₂²×#67	—	2	8	no	—
105	C₂²×#67	C₄×C₅	1	8	yes	complemented
106	C₂²×#67	C₂²×C₅	1	4	yes	—
107	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	complemented
109	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
111	C₂×#217	C₂²×C₅	1	2	yes	—
112	C₂×#217	C₂²×C₅	1	4	yes	complemented
113	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
114	D₃×C₂²⋊C₄	—	2	8	no	—
115	C₃⋊#95	C₂²×C₅	1	8	yes	complemented
116	C₂⁴×C₅	—	2	4	no	—
117	C₂⁴×C₅	—	3	2	no	—
118	C₂⁴×C₅	—	3	4	no	—
119	C₂⁴×C₅	—	3	8	no	—
120	C₂⁴×C₅	—	4	4	no	—
121	C₂⁴×C₅	—	12	4	no	—
122	C₂⁴×C₅	C₄×D₃	1	4	yes	complemented
123	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
124	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
125	C₂×C₅×D₄	—	3	16	no	—
126	C₂×C₅×D₄	—	6	32	no	—
127	C₂×C₅×D₄	—	6	8	no	—
128	C₂×C₅×D₄	—	6	8	no	—
129	C₂²×C₄×C₅	—	3	4	no	—
130	C₂²×C₄×C₅	—	3	2	no	—
131	C₂²×C₄×C₅	—	3	4	no	—
132	C₂²×C₄×C₅	—	6	8	no	—
133	C₂²×C₄×C₅	—	6	4	no	—
134	C₂²×C₄×C₅	—	12	8	no	—
135	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
136	C₅×C₂²⋊C₄	—	2	4	no	—
137	C₅×C₂²⋊C₄	—	4	4	no	—
138	C₅×C₂²⋊C₄	—	6	8	no	—
139	C₅×C₂²⋊C₄	—	6	4	no	—
140	C₅×C₂²⋊C₄	—	12	4	no	—
141	C₂³×D₄	—	3	1	no	—
142	C₂²×C₂²⋊C₄	—	3	2	no	—
143	#386	—	3	8	no	—
144	#381	—	3	2	no	—
145	#379	—	3	1	no	—
146	#379	C₅×D₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	2	8	no	—
149	C₂²×C₃×C₅	—	2	4	no	—
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	—	2	4	no	—
152	C₂²×C₃×C₅	—	4	16	no	—
153	C₂²×C₃×C₅	—	4	8	no	—
154	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
155	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
157	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
158	C₂×C₅×D₃	—	2	8	no	—
159	C₂×C₅×D₃	—	2	8	no	—
160	C₂×C₅×D₃	—	2	8	no	—
161	C₂×C₅×D₃	—	4	16	no	—
162	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	8	yes	—
163	C₃×C₄×C₅	—	4	4	no	—
164	C₅×Dic₃	—	2	4	no	—
165	C₅×Dic₃	—	4	4	no	—
166	C₂⁴×C₃	—	2	4	no	—
167	C₂⁴×C₃	—	4	4	no	—
168	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	complemented
169	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
170	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
171	C₂³×D₃	—	4	4	no	—
172	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
173	C₂³×D₃	C₅×D₄	1	8	yes	—
174	C₂³×D₃	C₂³×C₅	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
176	C₂×#67	—	2	32	no	—
177	C₂×#67	—	2	8	no	—
178	C₂×#67	—	2	8	no	—
179	C₂×#67	C₂×C₄×C₅	1	16	yes	complemented
180	C₂²×Dic₃	—	2	4	no	—
181	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
182	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
183	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
184	C₂×C₄×D₃	—	2	8	no	—
185	C₂×C₄×D₃	—	4	8	no	—
186	C₃×C₂²⋊C₄	—	2	4	no	—
187	C₃×C₂²⋊C₄	—	4	4	no	—
188	#217	—	2	4	no	—
189	#217	—	4	4	no	—
190	(C₂×D₃)⋊C₄	—	2	8	no	—
191	C₂³×C₅	—	2	4	no	—
192	C₂³×C₅	—	2	8	no	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	2	4	no	—
196	C₂³×C₅	—	3	4	no	—
197	C₂³×C₅	—	3	4	no	—
198	C₂³×C₅	—	3	4	no	—
199	C₂³×C₅	—	3	16	no	—
200	C₂³×C₅	—	4	8	no	—
201	C₂³×C₅	—	4	16	no	—
202	C₂³×C₅	—	6	8	no	—
203	C₂³×C₅	—	12	8	no	—
204	C₂³×C₅	—	12	16	no	—
205	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
206	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
207	C₂³×C₅	D₃×D₄	1	4	yes	—
208	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
209	C₅×D₄	—	6	32	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	8	no	—
212	C₂×C₄×C₅	—	3	4	no	—
213	C₂×C₄×C₅	—	6	8	no	—
214	C₂×C₄×C₅	—	6	4	no	—
215	C₂×C₄×C₅	—	6	4	no	—
216	C₂×C₄×C₅	—	6	8	no	—
217	C₂×C₄×C₅	—	12	16	no	—
218	C₂⁵	—	3	1	no	—
219	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
220	C₂²×D₄	—	3	8	no	—
221	C₂²×D₄	—	3	4	no	—
222	C₂²×D₄	—	6	8	no	—
223	C₂³×C₄	—	3	1	no	—
224	C₂³×C₄	—	3	4	no	—
225	C₂×C₂²⋊C₄	—	3	2	no	—
226	C₂×C₂²⋊C₄	—	3	4	no	—
227	C₂×C₂²⋊C₄	—	3	4	no	—
228	C₂×C₂²⋊C₄	—	6	8	no	—
229	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
230	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
231	#95	—	3	8	no	—
232	C₂×C₃×C₅	—	2	4	no	—
233	C₂×C₃×C₅	—	4	4	no	—
234	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₃×C₅	#518	1	2	yes	—
236	C₂×C₃×C₅	#534	1	4	yes	—
237	C₅×D₃	—	2	8	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	2	8	no	—
240	C₂³×C₃	—	2	4	no	—
241	C₂³×C₃	—	2	4	no	—
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	4	8	no	—
244	C₂³×C₃	—	4	16	no	—
245	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
246	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
247	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
248	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
249	C₂²×D₃	—	2	8	no	—
250	C₂²×D₃	—	4	8	no	—
251	C₂²×D₃	—	4	16	no	—
252	C₂²×D₃	C₅×C₂²⋊C₄	1	16	yes	complemented
253	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
254	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
255	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	8	no	—
258	#67	—	2	32	no	—
259	C₂×Dic₃	—	2	8	no	—
260	C₂×Dic₃	—	2	4	no	—
261	C₂×Dic₃	—	2	4	no	—
262	C₂×Dic₃	—	2	8	no	—
263	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
264	C₄×D₃	—	4	16	no	—
265	C₂²×C₅	—	2	4	no	—
266	C₂²×C₅	—	2	8	no	—
267	C₂²×C₅	—	2	4	no	—
268	C₂²×C₅	—	2	4	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	3	8	no	—
271	C₂²×C₅	—	4	16	no	—
272	C₂²×C₅	—	4	8	no	—
273	C₂²×C₅	—	6	8	no	—
274	C₂²×C₅	—	6	8	no	—
275	C₂²×C₅	—	6	8	no	—
276	C₂²×C₅	—	12	16	no	—
277	C₂²×C₅	D₃×C₂²⋊C₄	1	4	yes	—
278	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
279	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
280	C₂²×C₅	#1004	1	4	yes	—
281	C₄×C₅	—	4	4	no	—
282	C₄×C₅	—	6	4	no	—
283	C₄×C₅	—	12	4	no	—
284	C₂⁴	—	2	4	no	—
285	C₂⁴	—	3	2	no	—
286	C₂⁴	—	3	4	no	—
287	C₂⁴	—	3	8	no	—
288	C₂⁴	—	4	4	no	—
289	C₂⁴	—	12	4	no	—
290	C₂⁴	C₄×C₅×D₃	1	4	yes	complemented
291	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
292	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
293	C₂×D₄	—	3	16	no	—
294	C₂×D₄	—	6	32	no	—
295	C₂×D₄	—	6	8	no	—
296	C₂×D₄	—	6	8	no	—
297	C₂²×C₄	—	3	4	no	—
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	—	3	4	no	—
300	C₂²×C₄	—	6	8	no	—
301	C₂²×C₄	—	6	4	no	—
302	C₂²×C₄	—	12	8	no	—
303	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	6	8	no	—
307	C₂²⋊C₄	—	6	4	no	—
308	C₂²⋊C₄	—	12	4	no	—
309	C₃×C₅	#2308	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	4	no	—
311	C₂²×C₃	—	2	8	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	4	16	no	—
316	C₂²×C₃	—	4	8	no	—
317	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
318	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
319	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
320	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
321	C₂×D₃	—	2	8	no	—
322	C₂×D₃	—	2	8	no	—
323	C₂×D₃	—	2	8	no	—
324	C₂×D₃	—	4	16	no	—
325	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
326	C₃×C₄	—	4	4	no	—
327	Dic₃	—	2	4	no	—
328	Dic₃	—	4	4	no	—
329	C₂×C₅	—	2	4	no	—
330	C₂×C₅	—	4	4	no	—
331	C₂×C₅	—	6	8	no	—
332	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×C₅	#5486	1	2	yes	—
334	C₂×C₅	#5589	1	4	yes	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	3	4	no	—
341	C₂³	—	3	4	no	—
342	C₂³	—	3	4	no	—
343	C₂³	—	3	16	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	16	no	—
346	C₂³	—	6	8	no	—
347	C₂³	—	12	8	no	—
348	C₂³	—	12	16	no	—
349	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
350	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
351	C₂³	C₅×D₃×D₄	1	4	yes	—
352	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
353	D₄	—	6	32	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	3	4	no	—
357	C₂×C₄	—	6	8	no	—
358	C₂×C₄	—	6	4	no	—
359	C₂×C₄	—	6	4	no	—
360	C₂×C₄	—	6	8	no	—
361	C₂×C₄	—	12	16	no	—
362	C₂×C₃	—	2	4	no	—
363	C₂×C₃	—	4	4	no	—
364	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₃	C₅×#518	1	2	yes	—
366	C₂×C₃	C₅×#534	1	4	yes	—
367	D₃	—	2	8	no	—
368	C₅	#73849	1	1	yes	characteristic, direct product factor, Sylow
369	C₂²	—	2	4	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	3	8	no	—
375	C₂²	—	4	16	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	6	8	no	—
378	C₂²	—	6	8	no	—
379	C₂²	—	6	8	no	—
380	C₂²	—	12	16	no	—
381	C₂²	C₅×D₃×C₂²⋊C₄	1	4	yes	—
382	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
383	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
384	C₂²	C₅×#1004	1	4	yes	—
385	C₄	—	4	4	no	—
386	C₄	—	6	4	no	—
387	C₄	—	12	4	no	—
388	C₃	C₅×#2308	1	1	yes	characteristic, complemented, Sylow
389	C₂	—	2	4	no	—
390	C₂	—	4	4	no	—
391	C₂	—	6	8	no	—
392	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
393	C₂	C₅×#5486	1	2	yes	—
394	C₂	C₅×#5589	1	4	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#379	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×#67	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#379	D₃
hypocenter	C₃	C₅×#2308
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#379

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
3. C₃×C₅×#379	C₂	semidirect
4. C₅×#5247	C₂	semidirect
5. C₅×#4956	C₂	semidirect
6. C₅×#4943	C₂	semidirect
11. C₂²×C₅×#67	C₄	semidirect
14. C₂²×C₄×C₅×D₃	C₂²	semidirect
16. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
18. C₂×C₅×#217	C₂²	semidirect
19. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₅×C₃⋊#95	C₂²	semidirect
22. #73849	C₅	direct (N × H)
28. C₅×#379	D₃	semidirect
31. C₂⁴×C₃×C₅	C₂×C₄	semidirect
42. C₂×C₅×#67	C₂×C₄	semidirect
44. C₂²×C₅×Dic₃	C₂×C₄	semidirect
55. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
56. C₃×#379	C₂×C₅	semidirect
57. #5247	C₂×C₅	semidirect
58. #4956	C₂×C₅	semidirect
59. #4943	C₂×C₅	semidirect
72. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
89. C₂²×C₅×D₃	C₂²⋊C₄	semidirect
105. C₂²×#67	C₄×C₅	semidirect
108. C₂²×C₄×D₃	C₂²×C₅	semidirect
110. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
112. C₂×#217	C₂²×C₅	semidirect
113. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
115. C₃⋊#95	C₂²×C₅	semidirect
122. C₂⁴×C₅	C₄×D₃	semidirect
146. #379	C₅×D₃	semidirect
168. C₂⁴×C₃	C₂×C₄×C₅	semidirect
179. C₂×#67	C₂×C₄×C₅	semidirect
181. C₂²×Dic₃	C₂×C₄×C₅	semidirect
230. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
252. C₂²×D₃	C₅×C₂²⋊C₄	semidirect
290. C₂⁴	C₄×C₅×D₃	semidirect
309. C₃×C₅	#2308	semidirect
368. C₅	#73849	direct (N × H)
388. C₃	C₅×#2308	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×#67	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₃×C₅×#379	2
C₅×#5247	2
C₅×#4956	2
C₅×#4943	2
C₅×#2308	3
#73849	5

Subgroups — C5×#73849 #14322380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73849 #14322380