Subgroups — C₃×C₅×#2379 #14275413

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#386	C₂	1	2	yes	maximal
5	C₃×C₅×#385	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#382	C₂	1	2	yes	maximal, complemented
7	C₅×#2379	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
11	C₃×C₅×#124	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#95	C₂²	1	4	yes	—
21	C₃×C₅×#95	C₂²	1	4	yes	—
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×#2379	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
25	C₅×#391	C₂×C₃	1	2	yes	complemented
26	C₅×#388	C₂×C₃	1	4	yes	complemented
27	C₅×#386	C₂×C₃	1	2	yes	—
28	C₅×#385	C₂×C₃	1	4	yes	complemented
29	C₅×#382	C₂×C₃	1	2	yes	complemented
30	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
31	C₂×C₃×C₅×Q₈	—	4	1	no	—
32	C₂×C₃×C₅×Q₈	—	4	1	no	—
33	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
34	C₂×C₃×C₅×D₄	—	4	1	no	—
35	C₂×C₃×C₅×D₄	—	4	1	no	—
36	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	—	4	4	no	—
38	C₂²×C₃×C₄×C₅	—	4	2	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×C₄⋊C₄	—	4	2	no	—
45	C₃×C₅×C₄⋊C₄	—	4	2	no	—
46	C₃×C₅×C₄⋊C₄	—	4	2	no	—
47	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
48	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
49	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
50	C₃×C₄²×C₅	—	4	2	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
52	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
53	C₃×#391	C₂×C₅	1	2	yes	complemented
54	C₃×#388	C₂×C₅	1	4	yes	complemented
55	C₃×#386	C₂×C₅	1	2	yes	—
56	C₃×#385	C₂×C₅	1	4	yes	complemented
57	C₃×#382	C₂×C₅	1	2	yes	complemented
58	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
59	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
60	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
61	C₅×#124	C₃×C₄	1	8	yes	complemented
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
66	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
68	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₅×#95	C₂²×C₃	1	4	yes	—
71	C₅×#95	C₂²×C₃	1	4	yes	—
72	C₅×#95	C₂²×C₃	1	4	yes	—
73	#2379	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
79	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₃×C₅×Q₈	—	4	4	no	—
81	C₃×C₅×D₄	—	4	4	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	4	8	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
98	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
99	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
100	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
101	C₃×#124	C₄×C₅	1	8	yes	complemented
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
108	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₃×#95	C₂²×C₅	1	4	yes	—
111	C₃×#95	C₂²×C₅	1	4	yes	—
112	C₃×#95	C₂²×C₅	1	4	yes	—
113	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
114	C₂×C₅×Q₈	—	4	1	no	—
115	C₂×C₅×Q₈	—	4	1	no	—
116	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂×C₅×D₄	—	4	1	no	—
119	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
120	C₂²×C₄×C₅	—	4	4	no	—
121	C₂²×C₄×C₅	—	4	2	no	—
122	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
126	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
127	C₅×C₄⋊C₄	—	4	2	no	—
128	C₅×C₄⋊C₄	—	4	2	no	—
129	C₅×C₄⋊C₄	—	4	2	no	—
130	C₅×C₂²⋊C₄	—	4	2	no	—
131	C₅×C₂²⋊C₄	—	4	4	no	—
132	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
133	C₄²×C₅	—	4	2	no	—
134	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
135	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
136	#391	C₂×C₃×C₅	1	2	yes	complemented
137	#388	C₂×C₃×C₅	1	4	yes	complemented
138	#386	C₂×C₃×C₅	1	2	yes	—
139	#385	C₂×C₃×C₅	1	4	yes	complemented
140	#382	C₂×C₃×C₅	1	2	yes	complemented
141	C₂²×C₃×C₅	—	2	4	no	—
142	C₂²×C₃×C₅	—	2	8	no	—
143	C₂²×C₃×C₅	—	4	2	no	—
144	C₂²×C₃×C₅	—	4	4	no	—
145	C₂²×C₃×C₅	—	4	2	no	—
146	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
147	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
150	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
151	C₃×C₄×C₅	—	2	2	no	—
152	C₃×C₄×C₅	—	2	4	no	—
153	C₃×C₄×C₅	—	2	4	no	—
154	C₃×C₄×C₅	—	4	4	no	—
155	C₃×C₄×C₅	—	4	4	no	—
156	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
157	C₂×C₃×Q₈	—	4	1	no	—
158	C₂×C₃×Q₈	—	4	1	no	—
159	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
160	C₂×C₃×D₄	—	4	1	no	—
161	C₂×C₃×D₄	—	4	1	no	—
162	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
163	C₂²×C₃×C₄	—	4	4	no	—
164	C₂²×C₃×C₄	—	4	2	no	—
165	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
169	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
170	C₃×C₄⋊C₄	—	4	2	no	—
171	C₃×C₄⋊C₄	—	4	2	no	—
172	C₃×C₄⋊C₄	—	4	2	no	—
173	C₃×C₂²⋊C₄	—	4	2	no	—
174	C₃×C₂²⋊C₄	—	4	4	no	—
175	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
176	C₃×C₄²	—	4	2	no	—
177	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
178	C₂³×C₅	—	2	4	no	—
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	2	4	no	—
182	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
183	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
184	C₅×Q₈	—	4	4	no	—
185	C₅×D₄	—	4	4	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	—	2	4	no	—
198	C₂×C₄×C₅	—	4	8	no	—
199	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
200	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
202	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
203	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
204	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
205	#124	C₃×C₄×C₅	1	8	yes	complemented
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
207	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
210	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
211	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
212	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
213	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
214	#95	C₂²×C₃×C₅	1	4	yes	—
215	#95	C₂²×C₃×C₅	1	4	yes	—
216	#95	C₂²×C₃×C₅	1	4	yes	—
217	C₂×C₃×C₅	—	4	4	no	—
218	C₂×C₃×C₅	#518	1	1	yes	characteristic
219	C₂×C₃×C₅	#520	1	2	yes	—
220	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
221	C₂×C₃×C₅	#562	1	2	yes	—
222	C₂×C₃×C₅	#563	1	1	yes	characteristic
223	C₂³×C₃	—	2	4	no	—
224	C₂³×C₃	—	2	2	no	—
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	—	2	4	no	—
227	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
228	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
229	C₃×Q₈	—	4	4	no	—
230	C₃×D₄	—	4	4	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	4	8	no	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
245	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
246	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
247	C₂²×C₅	—	2	4	no	—
248	C₂²×C₅	—	2	8	no	—
249	C₂²×C₅	—	4	2	no	—
250	C₂²×C₅	—	4	4	no	—
251	C₂²×C₅	—	4	2	no	—
252	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
253	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
254	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	2	4	no	—
260	C₄×C₅	—	4	4	no	—
261	C₄×C₅	—	4	4	no	—
262	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
266	C₂×D₄	—	4	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
272	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
273	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
275	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
276	C₄⋊C₄	—	4	2	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₂²⋊C₄	—	4	2	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	16	yes	complemented
282	C₄²	—	4	2	no	—
283	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
284	C₃×C₅	#2379	1	1	yes	characteristic, direct product factor, Hall
285	C₂²×C₃	—	2	4	no	—
286	C₂²×C₃	—	2	8	no	—
287	C₂²×C₃	—	4	2	no	—
288	C₂²×C₃	—	4	4	no	—
289	C₂²×C₃	—	4	2	no	—
290	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
291	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
293	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
294	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	4	4	no	—
299	C₃×C₄	—	4	4	no	—
300	C₂×C₅	—	4	4	no	—
301	C₂×C₅	C₃×#518	1	1	yes	characteristic
302	C₂×C₅	C₃×#520	1	2	yes	—
303	C₂×C₅	C₃×H(3,𝔽₄)	1	1	yes	characteristic
304	C₂×C₅	C₃×#562	1	2	yes	—
305	C₂×C₅	C₃×#563	1	1	yes	characteristic
306	C₂³	—	2	4	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	4	no	—
310	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
311	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
312	Q₈	—	4	4	no	—
313	D₄	—	4	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
328	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
329	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
330	C₂×C₃	—	4	4	no	—
331	C₂×C₃	C₅×#518	1	1	yes	characteristic
332	C₂×C₃	C₅×#520	1	2	yes	—
333	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
334	C₂×C₃	C₅×#562	1	2	yes	—
335	C₂×C₃	C₅×#563	1	1	yes	characteristic
336	C₅	C₃×#2379	1	1	yes	characteristic, direct product factor, Sylow
337	C₂²	—	2	4	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	2	no	—
342	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
343	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
346	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
347	C₄	—	2	2	no	—
348	C₄	—	2	4	no	—
349	C₄	—	2	4	no	—
350	C₄	—	4	4	no	—
351	C₄	—	4	4	no	—
352	C₃	C₅×#2379	1	1	yes	characteristic, direct product factor, Sylow
353	C₂	—	4	4	no	—
354	C₂	C₃×C₅×#518	1	1	yes	characteristic
355	C₂	C₃×C₅×#520	1	2	yes	—
356	C₂	C₃×C₅×H(3,𝔽₄)	1	1	yes	characteristic
357	C₂	C₃×C₅×#562	1	2	yes	—
358	C₂	C₃×C₅×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#391	C₂	semidirect
3. C₃×C₅×#388	C₂	semidirect
5. C₃×C₅×#385	C₂	semidirect
6. C₃×C₅×#382	C₂	semidirect
7. C₅×#2379	C₃	direct (N × H)
11. C₃×C₅×#124	C₄	semidirect
23. C₃×#2379	C₅	direct (N × H)
25. C₅×#391	C₂×C₃	semidirect
26. C₅×#388	C₂×C₃	semidirect
28. C₅×#385	C₂×C₃	semidirect
29. C₅×#382	C₂×C₃	semidirect
33. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
49. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
51. C₃×C₄²×C₅	C₂×C₄	semidirect
53. C₃×#391	C₂×C₅	semidirect
54. C₃×#388	C₂×C₅	semidirect
56. C₃×#385	C₂×C₅	semidirect
57. C₃×#382	C₂×C₅	semidirect
61. C₅×#124	C₃×C₄	semidirect
73. #2379	C₃×C₅	direct (N × H)
101. C₃×#124	C₄×C₅	semidirect
116. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
132. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
134. C₄²×C₅	C₂×C₃×C₄	semidirect
136. #391	C₂×C₃×C₅	semidirect
137. #388	C₂×C₃×C₅	semidirect
139. #385	C₂×C₃×C₅	semidirect
140. #382	C₂×C₃×C₅	semidirect
159. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
175. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
177. C₃×C₄²	C₂×C₄×C₅	semidirect
205. #124	C₃×C₄×C₅	semidirect
265. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
281. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
283. C₄²	C₂×C₃×C₄×C₅	semidirect
284. C₃×C₅	#2379	direct (N × H)
336. C₅	C₃×#2379	direct (N × H)
352. C₃	C₅×#2379	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#124	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#382	2
C₅×#2379	3
C₃×#2379	5

Subgroups — C3×C5×#2379 #14275413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2379 #14275413