Subgroups — C₃×C₅×#2507 #14275541

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#398	C₂	1	2	yes	maximal
2	C₃×C₅×#398	C₂	1	2	yes	maximal
3	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#389	C₂	1	2	yes	maximal
8	C₃×C₅×#387	C₂	1	2	yes	maximal
9	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2507	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×C₅×#95	C₂²	1	2	yes	—
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×#2507	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#398	C₂×C₃	1	2	yes	—
38	C₅×#398	C₂×C₃	1	2	yes	—
39	C₅×#389	C₂×C₃	1	1	yes	characteristic
40	C₅×#389	C₂×C₃	1	1	yes	characteristic
41	C₅×#389	C₂×C₃	1	1	yes	characteristic
42	C₅×#389	C₂×C₃	1	1	yes	characteristic
43	C₅×#389	C₂×C₃	1	2	yes	—
44	C₅×#387	C₂×C₃	1	2	yes	—
45	C₅×#384	C₂×C₃	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	4	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	4	2	no	—
65	C₃×C₅×C₄⋊C₄	—	4	2	no	—
66	C₃×C₅×C₄⋊C₄	—	4	2	no	—
67	C₃×C₅×C₄⋊C₄	—	4	2	no	—
68	C₃×C₅×C₄⋊C₄	—	4	2	no	—
69	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	—
70	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	—
71	C₃×C₄²×C₅	—	2	2	no	—
72	C₃×C₄²×C₅	—	2	2	no	—
73	C₃×C₄²×C₅	—	2	2	no	—
74	C₃×C₄²×C₅	—	4	2	no	—
75	C₃×#398	C₂×C₅	1	2	yes	—
76	C₃×#398	C₂×C₅	1	2	yes	—
77	C₃×#389	C₂×C₅	1	2	yes	—
78	C₃×#389	C₂×C₅	1	1	yes	characteristic
79	C₃×#389	C₂×C₅	1	1	yes	characteristic
80	C₃×#389	C₂×C₅	1	1	yes	characteristic
81	C₃×#389	C₂×C₅	1	1	yes	characteristic
82	C₃×#387	C₂×C₅	1	2	yes	—
83	C₃×#384	C₂×C₅	1	1	yes	characteristic
84	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
85	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
102	C₅×#95	C₂²×C₃	1	1	yes	characteristic
103	C₅×#95	C₂²×C₃	1	1	yes	characteristic
104	C₅×#95	C₂²×C₃	1	2	yes	—
105	C₅×#95	C₂²×C₃	1	2	yes	—
106	C₅×#95	C₂²×C₃	1	2	yes	—
107	C₅×#95	C₂²×C₃	1	2	yes	—
108	C₅×#95	C₂²×C₃	1	2	yes	—
109	#2507	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	—	2	1	no	—
112	C₂×C₃×C₄×C₅	—	2	1	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	1	no	—
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	1	no	—
120	C₂×C₃×C₄×C₅	—	2	1	no	—
121	C₂×C₃×C₄×C₅	—	2	1	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	1	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
138	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	#41	1	2	yes	—
143	C₂×C₃×C₄×C₅	#41	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
160	C₃×#95	C₂²×C₅	1	1	yes	characteristic
161	C₃×#95	C₂²×C₅	1	1	yes	characteristic
162	C₃×#95	C₂²×C₅	1	2	yes	—
163	C₃×#95	C₂²×C₅	1	2	yes	—
164	C₃×#95	C₂²×C₅	1	2	yes	—
165	C₃×#95	C₂²×C₅	1	2	yes	—
166	C₃×#95	C₂²×C₅	1	2	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	2	4	no	—
180	C₅×C₄⋊C₄	—	2	2	no	—
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	—	4	2	no	—
184	C₅×C₄⋊C₄	—	4	2	no	—
185	C₅×C₄⋊C₄	—	4	2	no	—
186	C₅×C₄⋊C₄	—	4	2	no	—
187	C₅×C₄⋊C₄	—	4	2	no	—
188	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	—
189	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	—
190	C₄²×C₅	—	2	2	no	—
191	C₄²×C₅	—	2	2	no	—
192	C₄²×C₅	—	2	2	no	—
193	C₄²×C₅	—	4	2	no	—
194	#398	C₂×C₃×C₅	1	2	yes	—
195	#398	C₂×C₃×C₅	1	2	yes	—
196	#389	C₂×C₃×C₅	1	2	yes	—
197	#389	C₂×C₃×C₅	1	1	yes	characteristic
198	#389	C₂×C₃×C₅	1	1	yes	characteristic
199	#389	C₂×C₃×C₅	1	1	yes	characteristic
200	#389	C₂×C₃×C₅	1	1	yes	characteristic
201	#387	C₂×C₃×C₅	1	2	yes	—
202	#384	C₂×C₃×C₅	1	1	yes	characteristic
203	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
205	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
206	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
207	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
208	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
209	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
210	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	2	no	—
214	C₃×C₄×C₅	—	2	2	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	4	no	—
217	C₃×C₄×C₅	—	4	1	no	—
218	C₃×C₄×C₅	—	4	2	no	—
219	C₃×C₄×C₅	—	4	2	no	—
220	C₃×C₄×C₅	—	4	1	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	#125	1	4	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
232	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	2	4	no	—
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	2	2	no	—
238	C₃×C₄⋊C₄	—	2	2	no	—
239	C₃×C₄⋊C₄	—	4	2	no	—
240	C₃×C₄⋊C₄	—	4	2	no	—
241	C₃×C₄⋊C₄	—	4	2	no	—
242	C₃×C₄⋊C₄	—	4	2	no	—
243	C₃×C₄⋊C₄	—	4	2	no	—
244	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	—
245	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	—
246	C₃×C₄²	—	2	2	no	—
247	C₃×C₄²	—	2	2	no	—
248	C₃×C₄²	—	2	2	no	—
249	C₃×C₄²	—	4	2	no	—
250	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	1	no	—
253	C₂×C₄×C₅	—	2	1	no	—
254	C₂×C₄×C₅	—	2	1	no	—
255	C₂×C₄×C₅	—	2	1	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	1	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	1	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	1	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
277	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
278	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
279	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
280	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
281	C₂×C₄×C₅	C₃×#41	1	2	yes	—
282	C₂×C₄×C₅	C₃×#41	1	2	yes	—
283	C₂×C₄×C₅	C₃×#41	1	2	yes	—
284	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
289	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
290	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
291	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
292	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
293	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
294	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
297	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
298	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
300	#95	C₂²×C₃×C₅	1	1	yes	characteristic
301	#95	C₂²×C₃×C₅	1	1	yes	characteristic
302	#95	C₂²×C₃×C₅	1	2	yes	—
303	#95	C₂²×C₃×C₅	1	2	yes	—
304	#95	C₂²×C₃×C₅	1	2	yes	—
305	#95	C₂²×C₃×C₅	1	2	yes	—
306	#95	C₂²×C₃×C₅	1	2	yes	—
307	C₂×C₃×C₅	C₂×#125	1	1	yes	characteristic
308	C₂×C₃×C₅	#533	1	1	yes	characteristic
309	C₂×C₃×C₅	#540	1	1	yes	characteristic
310	C₂×C₃×C₅	#553	1	1	yes	characteristic
311	C₂×C₃×C₅	#554	1	1	yes	characteristic
312	C₂×C₃×C₅	#554	1	1	yes	characteristic
313	C₂×C₃×C₅	Q₈²	1	1	yes	characteristic
314	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
341	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
342	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
344	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
345	C₂×C₃×C₄	C₅×#41	1	2	yes	—
346	C₂×C₃×C₄	C₅×#41	1	2	yes	—
347	C₂×C₃×C₄	C₅×#41	1	2	yes	—
348	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
349	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
350	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
351	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
352	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
353	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	—	2	2	no	—
359	C₄×C₅	—	2	4	no	—
360	C₄×C₅	—	4	1	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	—	4	2	no	—
363	C₄×C₅	—	4	1	no	—
364	C₄×C₅	—	4	2	no	—
365	C₄×C₅	C₃×#125	1	4	yes	—
366	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
367	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
368	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
369	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
370	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
371	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
372	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
373	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
374	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
375	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
376	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	—
388	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	4	2	no	—
393	C₃×C₅	#2507	1	1	yes	characteristic, direct product factor, Hall
394	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
395	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
396	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
397	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
398	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
399	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	2	2	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	4	no	—
406	C₃×C₄	—	4	1	no	—
407	C₃×C₄	—	4	2	no	—
408	C₃×C₄	—	4	2	no	—
409	C₃×C₄	—	4	1	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	C₅×#125	1	4	yes	—
412	C₂×C₅	C₂×C₃×#125	1	1	yes	characteristic
413	C₂×C₅	C₃×#533	1	1	yes	characteristic
414	C₂×C₅	C₃×#540	1	1	yes	characteristic
415	C₂×C₅	C₃×#553	1	1	yes	characteristic
416	C₂×C₅	C₃×#554	1	1	yes	characteristic
417	C₂×C₅	C₃×#554	1	1	yes	characteristic
418	C₂×C₅	C₃×Q₈²	1	1	yes	characteristic
419	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
446	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
447	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
448	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
449	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
450	C₂×C₄	C₃×C₅×#41	1	2	yes	—
451	C₂×C₄	C₃×C₅×#41	1	2	yes	—
452	C₂×C₄	C₃×C₅×#41	1	2	yes	—
453	C₂×C₃	C₂×C₅×#125	1	1	yes	characteristic
454	C₂×C₃	C₅×#533	1	1	yes	characteristic
455	C₂×C₃	C₅×#540	1	1	yes	characteristic
456	C₂×C₃	C₅×#553	1	1	yes	characteristic
457	C₂×C₃	C₅×#554	1	1	yes	characteristic
458	C₂×C₃	C₅×#554	1	1	yes	characteristic
459	C₂×C₃	C₅×Q₈²	1	1	yes	characteristic
460	C₅	C₃×#2507	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
462	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
463	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
464	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
465	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
466	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	2	no	—
478	C₄	C₃×C₅×#125	1	4	yes	—
479	C₃	C₅×#2507	1	1	yes	characteristic, direct product factor, Sylow
480	C₂	C₂×C₃×C₅×#125	1	1	yes	characteristic
481	C₂	C₃×C₅×#533	1	1	yes	characteristic
482	C₂	C₃×C₅×#540	1	1	yes	characteristic
483	C₂	C₃×C₅×#553	1	1	yes	characteristic
484	C₂	C₃×C₅×#554	1	1	yes	characteristic
485	C₂	C₃×C₅×#554	1	1	yes	characteristic
486	C₂	C₃×C₅×Q₈²	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
12. C₅×#2507	C₃	direct (N × H)
36. C₃×#2507	C₅	direct (N × H)
109. #2507	C₃×C₅	direct (N × H)
393. C₃×C₅	#2507	direct (N × H)
460. C₅	C₃×#2507	direct (N × H)
479. C₃	C₅×#2507	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#398	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#384	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2507	3
C₃×#2507	5

Subgroups — C3×C5×#2507 #14275541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2507 #14275541