Subgroups — C₃×C₅×#3125 #14276159

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3125	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#126	—	2	1	no	—
24	C₃×C₅×#124	—	2	1	no	—
25	C₃×C₅×#124	C₂²	1	1	yes	characteristic
26	C₃×C₅×#123	—	2	1	no	—
27	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×#121	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×D₄	—	2	1	no	—
34	C₃×C₄×C₅×D₄	—	2	1	no	—
35	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₅×#117	—	2	1	no	—
39	C₃×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×C₅×#106	C₂²	1	1	yes	characteristic
43	C₃×C₅×#106	C₂²	1	1	yes	characteristic
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic
50	C₃×C₅×#103	C₂²	1	1	yes	characteristic
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×#97	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
60	C₃×#3125	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#481	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#449	C₂×C₃	1	1	yes	characteristic
71	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
74	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	2	2	no	—
77	C₃×C₅×#41	—	2	2	no	—
78	C₂×C₃×C₅×Q₈	—	2	1	no	—
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	—	2	1	no	—
86	C₂²×C₃×C₄×C₅	—	2	1	no	—
87	C₂²×C₃×C₄×C₅	—	2	1	no	—
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₃×C₅×Q₁₆	—	2	2	no	—
92	C₃×C₅×SD₁₆	—	2	2	no	—
93	C₃×C₅×SD₁₆	—	2	2	no	—
94	C₃×C₅×D₈	—	2	2	no	—
95	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₃×C₅×C₄⋊C₄	—	2	1	no	—
100	C₃×C₅×C₄⋊C₄	—	2	1	no	—
101	C₃×C₅×C₄⋊C₄	—	2	1	no	—
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
103	C₃×C₅×C₄⋊C₄	—	2	1	no	—
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₃×C₄²×C₅	—	2	1	no	—
121	C₃×C₄²×C₅	—	2	1	no	—
122	C₃×C₄²×C₅	—	2	1	no	—
123	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₃×#542	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#520	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#481	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#449	C₂×C₅	1	1	yes	characteristic
135	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
145	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
146	C₅×#126	—	2	1	no	—
147	C₅×#124	—	2	1	no	—
148	C₅×#124	C₂²×C₃	1	1	yes	characteristic
149	C₅×#123	—	2	1	no	—
150	C₅×C₂²⋊Q₈	—	2	1	no	—
151	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₅×#121	C₂²×C₃	1	1	yes	characteristic
153	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
154	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
155	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
156	C₄×C₅×D₄	—	2	1	no	—
157	C₄×C₅×D₄	—	2	1	no	—
158	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
160	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₅×#117	—	2	1	no	—
162	C₅×#117	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	—	2	1	no	—
164	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₅×#106	C₂²×C₃	1	1	yes	characteristic
166	C₅×#106	C₂²×C₃	1	1	yes	characteristic
167	C₅×#106	C₂²×C₃	1	1	yes	characteristic
168	C₅×#106	C₂²×C₃	1	1	yes	characteristic
169	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
170	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	C₅×#103	C₂²×C₃	1	1	yes	characteristic
172	C₅×#103	C₂²×C₃	1	1	yes	characteristic
173	C₅×#103	C₂²×C₃	1	1	yes	characteristic
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic
175	C₅×#102	C₂²×C₃	1	1	yes	characteristic
176	C₅×#102	C₂²×C₃	1	1	yes	characteristic
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic
179	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
180	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
181	C₅×#97	C₂²×C₃	1	1	yes	characteristic
182	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
183	#3125	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
187	C₃×C₅×Q₈	—	2	1	no	—
188	C₃×C₅×Q₈	—	2	1	no	—
189	C₃×C₅×Q₈	—	2	1	no	—
190	C₃×C₅×Q₈	—	8	1	no	—
191	C₃×C₅×Q₈	#41	1	2	yes	—
192	C₃×C₅×D₄	—	2	4	no	—
193	C₃×C₅×D₄	—	2	1	no	—
194	C₃×C₅×D₄	—	2	1	no	—
195	C₃×C₅×D₄	—	2	1	no	—
196	C₃×C₅×D₄	—	8	1	no	—
197	C₃×C₅×D₄	#41	1	2	yes	—
198	C₂×C₃×C₄×C₅	—	2	4	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	8	1	no	—
208	C₂×C₃×C₄×C₅	—	8	1	no	—
209	C₂×C₃×C₄×C₅	—	8	1	no	—
210	C₂×C₃×C₄×C₅	—	8	1	no	—
211	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
214	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
215	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₃×C₅×C₈	—	2	1	no	—
218	C₃×C₅×C₈	—	2	1	no	—
219	C₃×C₅×C₈	—	2	1	no	—
220	C₃×C₅×C₈	—	2	1	no	—
221	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
226	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₃×#126	—	2	1	no	—
228	C₃×#124	—	2	1	no	—
229	C₃×#124	C₂²×C₅	1	1	yes	characteristic
230	C₃×#123	—	2	1	no	—
231	C₃×C₂²⋊Q₈	—	2	1	no	—
232	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₃×#121	C₂²×C₅	1	1	yes	characteristic
234	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₃×C₄×D₄	—	2	1	no	—
238	C₃×C₄×D₄	—	2	1	no	—
239	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
240	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
242	C₃×#117	—	2	1	no	—
243	C₃×#117	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×C₄⋊C₄	—	2	1	no	—
245	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₃×#106	C₂²×C₅	1	1	yes	characteristic
247	C₃×#106	C₂²×C₅	1	1	yes	characteristic
248	C₃×#106	C₂²×C₅	1	1	yes	characteristic
249	C₃×#106	C₂²×C₅	1	1	yes	characteristic
250	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
251	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	C₃×#103	C₂²×C₅	1	1	yes	characteristic
253	C₃×#103	C₂²×C₅	1	1	yes	characteristic
254	C₃×#103	C₂²×C₅	1	1	yes	characteristic
255	C₃×#103	C₂²×C₅	1	1	yes	characteristic
256	C₃×#102	C₂²×C₅	1	1	yes	characteristic
257	C₃×#102	C₂²×C₅	1	1	yes	characteristic
258	C₃×#102	C₂²×C₅	1	1	yes	characteristic
259	C₃×#102	C₂²×C₅	1	1	yes	characteristic
260	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
262	C₃×#97	C₂²×C₅	1	1	yes	characteristic
263	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
264	C₅×#41	—	2	2	no	—
265	C₅×#41	—	2	2	no	—
266	C₂×C₅×Q₈	—	2	1	no	—
267	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
268	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₅×D₄	—	2	1	no	—
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
273	C₂²×C₄×C₅	—	2	1	no	—
274	C₂²×C₄×C₅	—	2	1	no	—
275	C₂²×C₄×C₅	—	2	1	no	—
276	C₂²×C₄×C₅	—	2	1	no	—
277	C₂²×C₄×C₅	—	2	1	no	—
278	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
279	C₅×Q₁₆	—	2	2	no	—
280	C₅×SD₁₆	—	2	2	no	—
281	C₅×SD₁₆	—	2	2	no	—
282	C₅×D₈	—	2	2	no	—
283	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
287	C₅×C₄⋊C₄	—	2	1	no	—
288	C₅×C₄⋊C₄	—	2	1	no	—
289	C₅×C₄⋊C₄	—	2	1	no	—
290	C₅×C₄⋊C₄	—	2	1	no	—
291	C₅×C₄⋊C₄	—	2	1	no	—
292	C₅×C₄⋊C₄	—	2	1	no	—
293	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
296	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
297	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
298	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
299	C₅×C₂²⋊C₄	—	2	1	no	—
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	—	2	1	no	—
303	C₅×C₂²⋊C₄	—	2	1	no	—
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	2	1	no	—
306	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
307	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
308	C₄²×C₅	—	2	1	no	—
309	C₄²×C₅	—	2	1	no	—
310	C₄²×C₅	—	2	1	no	—
311	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
312	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
313	#542	C₂×C₃×C₅	1	1	yes	characteristic, complemented
314	#520	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
316	#481	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
318	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#449	C₂×C₃×C₅	1	1	yes	characteristic
323	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	C₂²×C₃×C₅	—	2	1	no	—
329	C₂²×C₃×C₅	—	2	2	no	—
330	C₂²×C₃×C₅	—	2	1	no	—
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	4	1	no	—
333	C₂²×C₃×C₅	—	4	1	no	—
334	C₂²×C₃×C₅	—	4	1	no	—
335	C₂²×C₃×C₅	—	4	1	no	—
336	C₂²×C₃×C₅	—	4	1	no	—
337	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
338	C₃×C₄×C₅	—	2	1	no	—
339	C₃×C₄×C₅	—	2	2	no	—
340	C₃×C₄×C₅	—	2	1	no	—
341	C₃×C₄×C₅	—	2	1	no	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	2	1	no	—
344	C₃×C₄×C₅	—	4	1	no	—
345	C₃×C₄×C₅	—	4	1	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₃×C₄×C₅	—	4	1	no	—
349	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
351	C₃×#41	—	2	2	no	—
352	C₃×#41	—	2	2	no	—
353	C₂×C₃×Q₈	—	2	1	no	—
354	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
355	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₃×D₄	—	2	1	no	—
357	C₂×C₃×D₄	—	2	1	no	—
358	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₃×C₄	—	2	1	no	—
361	C₂²×C₃×C₄	—	2	1	no	—
362	C₂²×C₃×C₄	—	2	1	no	—
363	C₂²×C₃×C₄	—	2	1	no	—
364	C₂²×C₃×C₄	—	2	1	no	—
365	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
366	C₃×Q₁₆	—	2	2	no	—
367	C₃×SD₁₆	—	2	2	no	—
368	C₃×SD₁₆	—	2	2	no	—
369	C₃×D₈	—	2	2	no	—
370	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
374	C₃×C₄⋊C₄	—	2	1	no	—
375	C₃×C₄⋊C₄	—	2	1	no	—
376	C₃×C₄⋊C₄	—	2	1	no	—
377	C₃×C₄⋊C₄	—	2	1	no	—
378	C₃×C₄⋊C₄	—	2	1	no	—
379	C₃×C₄⋊C₄	—	2	1	no	—
380	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
381	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
382	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
383	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
384	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
385	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₃×C₂²⋊C₄	—	2	1	no	—
387	C₃×C₂²⋊C₄	—	2	1	no	—
388	C₃×C₂²⋊C₄	—	2	1	no	—
389	C₃×C₂²⋊C₄	—	2	1	no	—
390	C₃×C₂²⋊C₄	—	2	1	no	—
391	C₃×C₂²⋊C₄	—	2	1	no	—
392	C₃×C₂²⋊C₄	—	2	1	no	—
393	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
394	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
395	C₃×C₄²	—	2	1	no	—
396	C₃×C₄²	—	2	1	no	—
397	C₃×C₄²	—	2	1	no	—
398	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
399	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
400	C₂³×C₅	—	2	1	no	—
401	C₂³×C₅	—	2	1	no	—
402	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
403	C₅×Q₈	—	2	1	no	—
404	C₅×Q₈	—	2	1	no	—
405	C₅×Q₈	—	2	1	no	—
406	C₅×Q₈	—	8	1	no	—
407	C₅×Q₈	C₃×#41	1	2	yes	—
408	C₅×D₄	—	2	4	no	—
409	C₅×D₄	—	2	1	no	—
410	C₅×D₄	—	2	1	no	—
411	C₅×D₄	—	2	1	no	—
412	C₅×D₄	—	8	1	no	—
413	C₅×D₄	C₃×#41	1	2	yes	—
414	C₂×C₄×C₅	—	2	4	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	—	2	1	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	no	—
423	C₂×C₄×C₅	—	8	1	no	—
424	C₂×C₄×C₅	—	8	1	no	—
425	C₂×C₄×C₅	—	8	1	no	—
426	C₂×C₄×C₅	—	8	1	no	—
427	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
428	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
429	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
430	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
431	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
432	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
433	C₅×C₈	—	2	1	no	—
434	C₅×C₈	—	2	1	no	—
435	C₅×C₈	—	2	1	no	—
436	C₅×C₈	—	2	1	no	—
437	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
438	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
439	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
440	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
441	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
442	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
443	#126	—	2	1	no	—
444	#124	—	2	1	no	—
445	#124	C₂²×C₃×C₅	1	1	yes	characteristic
446	#123	—	2	1	no	—
447	C₂²⋊Q₈	—	2	1	no	—
448	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
449	#121	C₂²×C₃×C₅	1	1	yes	characteristic
450	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
451	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
452	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
456	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
457	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
458	#117	—	2	1	no	—
459	#117	C₂²×C₃×C₅	1	1	yes	characteristic
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
462	#106	C₂²×C₃×C₅	1	1	yes	characteristic
463	#106	C₂²×C₃×C₅	1	1	yes	characteristic
464	#106	C₂²×C₃×C₅	1	1	yes	characteristic
465	#106	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
468	#103	C₂²×C₃×C₅	1	1	yes	characteristic
469	#103	C₂²×C₃×C₅	1	1	yes	characteristic
470	#103	C₂²×C₃×C₅	1	1	yes	characteristic
471	#103	C₂²×C₃×C₅	1	1	yes	characteristic
472	#102	C₂²×C₃×C₅	1	1	yes	characteristic
473	#102	C₂²×C₃×C₅	1	1	yes	characteristic
474	#102	C₂²×C₃×C₅	1	1	yes	characteristic
475	#102	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
478	#97	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₂×C₃×C₅	—	4	1	no	—
481	C₂×C₃×C₅	—	4	2	no	—
482	C₂×C₃×C₅	—	8	1	no	—
483	C₂×C₃×C₅	#525	1	1	yes	characteristic
484	C₂×C₃×C₅	#577	1	1	yes	characteristic
485	C₂×C₃×C₅	#577	1	1	yes	characteristic
486	C₂³×C₃	—	2	1	no	—
487	C₂³×C₃	—	2	1	no	—
488	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
489	C₃×Q₈	—	2	1	no	—
490	C₃×Q₈	—	2	1	no	—
491	C₃×Q₈	—	2	1	no	—
492	C₃×Q₈	—	8	1	no	—
493	C₃×Q₈	C₅×#41	1	2	yes	—
494	C₃×D₄	—	2	4	no	—
495	C₃×D₄	—	2	1	no	—
496	C₃×D₄	—	2	1	no	—
497	C₃×D₄	—	2	1	no	—
498	C₃×D₄	—	8	1	no	—
499	C₃×D₄	C₅×#41	1	2	yes	—
500	C₂×C₃×C₄	—	2	4	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	8	1	no	—
510	C₂×C₃×C₄	—	8	1	no	—
511	C₂×C₃×C₄	—	8	1	no	—
512	C₂×C₃×C₄	—	8	1	no	—
513	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
514	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
515	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
516	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
517	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
519	C₃×C₈	—	2	1	no	—
520	C₃×C₈	—	2	1	no	—
521	C₃×C₈	—	2	1	no	—
522	C₃×C₈	—	2	1	no	—
523	C₂²×C₅	—	2	1	no	—
524	C₂²×C₅	—	2	1	no	—
525	C₂²×C₅	—	2	1	no	—
526	C₂²×C₅	—	2	2	no	—
527	C₂²×C₅	—	4	1	no	—
528	C₂²×C₅	—	4	1	no	—
529	C₂²×C₅	—	4	1	no	—
530	C₂²×C₅	—	4	1	no	—
531	C₂²×C₅	—	4	1	no	—
532	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	—	2	1	no	—
535	C₄×C₅	—	2	1	no	—
536	C₄×C₅	—	2	1	no	—
537	C₄×C₅	—	2	1	no	—
538	C₄×C₅	—	2	2	no	—
539	C₄×C₅	—	4	1	no	—
540	C₄×C₅	—	4	1	no	—
541	C₄×C₅	—	4	1	no	—
542	C₄×C₅	—	4	1	no	—
543	C₄×C₅	—	4	1	no	—
544	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
545	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
546	#41	—	2	2	no	—
547	#41	—	2	2	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
550	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
554	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
561	Q₁₆	—	2	2	no	—
562	SD₁₆	—	2	2	no	—
563	SD₁₆	—	2	2	no	—
564	D₈	—	2	2	no	—
565	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
566	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
567	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
568	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
576	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
577	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
578	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
579	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
580	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
581	C₂²⋊C₄	—	2	1	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₂²⋊C₄	—	2	1	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
589	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
594	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
595	C₃×C₅	#3125	1	1	yes	characteristic, direct product factor, Hall
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	4	1	no	—
601	C₂²×C₃	—	4	1	no	—
602	C₂²×C₃	—	4	1	no	—
603	C₂²×C₃	—	4	1	no	—
604	C₂²×C₃	—	4	1	no	—
605	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
606	C₃×C₄	—	2	1	no	—
607	C₃×C₄	—	2	2	no	—
608	C₃×C₄	—	2	1	no	—
609	C₃×C₄	—	2	1	no	—
610	C₃×C₄	—	2	1	no	—
611	C₃×C₄	—	2	1	no	—
612	C₃×C₄	—	4	1	no	—
613	C₃×C₄	—	4	1	no	—
614	C₃×C₄	—	4	1	no	—
615	C₃×C₄	—	4	1	no	—
616	C₃×C₄	—	4	1	no	—
617	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
618	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
619	C₂×C₅	—	4	1	no	—
620	C₂×C₅	—	4	2	no	—
621	C₂×C₅	—	8	1	no	—
622	C₂×C₅	C₃×#525	1	1	yes	characteristic
623	C₂×C₅	C₃×#577	1	1	yes	characteristic
624	C₂×C₅	C₃×#577	1	1	yes	characteristic
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
628	Q₈	—	2	1	no	—
629	Q₈	—	2	1	no	—
630	Q₈	—	2	1	no	—
631	Q₈	—	8	1	no	—
632	Q₈	C₃×C₅×#41	1	2	yes	—
633	D₄	—	2	4	no	—
634	D₄	—	2	1	no	—
635	D₄	—	2	1	no	—
636	D₄	—	2	1	no	—
637	D₄	—	8	1	no	—
638	D₄	C₃×C₅×#41	1	2	yes	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	8	1	no	—
649	C₂×C₄	—	8	1	no	—
650	C₂×C₄	—	8	1	no	—
651	C₂×C₄	—	8	1	no	—
652	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
653	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
654	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
655	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
656	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
657	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
658	C₈	—	2	1	no	—
659	C₈	—	2	1	no	—
660	C₈	—	2	1	no	—
661	C₈	—	2	1	no	—
662	C₂×C₃	—	4	1	no	—
663	C₂×C₃	—	4	2	no	—
664	C₂×C₃	—	8	1	no	—
665	C₂×C₃	C₅×#525	1	1	yes	characteristic
666	C₂×C₃	C₅×#577	1	1	yes	characteristic
667	C₂×C₃	C₅×#577	1	1	yes	characteristic
668	C₅	C₃×#3125	1	1	yes	characteristic, direct product factor, Sylow
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
691	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
692	C₃	C₅×#3125	1	1	yes	characteristic, direct product factor, Sylow
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	8	1	no	—
696	C₂	C₃×C₅×#525	1	1	yes	characteristic
697	C₂	C₃×C₅×#577	1	1	yes	characteristic
698	C₂	C₃×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#542	C₂	semidirect
2. C₃×C₅×#520	C₂	semidirect
3. C₃×C₅×#483	C₂	semidirect
4. C₃×C₅×#481	C₂	semidirect
5. C₃×C₅×#476	C₂	semidirect
6. C₃×C₅×#475	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#442	C₂	semidirect
12. C₃×C₅×#441	C₂	semidirect
13. C₃×C₄×C₅×SD₁₆	C₂	semidirect
14. C₃×C₄×C₅×SD₁₆	C₂	semidirect
15. C₃×C₅×#433	C₂	semidirect
16. C₅×#3125	C₃	direct (N × H)
60. C₃×#3125	C₅	direct (N × H)
61. C₅×#542	C₂×C₃	semidirect
62. C₅×#520	C₂×C₃	semidirect
63. C₅×#483	C₂×C₃	semidirect
64. C₅×#481	C₂×C₃	semidirect
65. C₅×#476	C₂×C₃	semidirect
66. C₅×#475	C₂×C₃	semidirect
67. C₅×#464	C₂×C₃	semidirect
68. C₅×#463	C₂×C₃	semidirect
69. C₅×#452	C₂×C₃	semidirect
71. C₅×#442	C₂×C₃	semidirect
72. C₅×#441	C₂×C₃	semidirect
73. C₄×C₅×SD₁₆	C₂×C₃	semidirect
74. C₄×C₅×SD₁₆	C₂×C₃	semidirect
75. C₅×#433	C₂×C₃	semidirect
125. C₃×#542	C₂×C₅	semidirect
126. C₃×#520	C₂×C₅	semidirect
127. C₃×#483	C₂×C₅	semidirect
128. C₃×#481	C₂×C₅	semidirect
129. C₃×#476	C₂×C₅	semidirect
130. C₃×#475	C₂×C₅	semidirect
131. C₃×#464	C₂×C₅	semidirect
132. C₃×#463	C₂×C₅	semidirect
133. C₃×#452	C₂×C₅	semidirect
135. C₃×#442	C₂×C₅	semidirect
136. C₃×#441	C₂×C₅	semidirect
137. C₃×C₄×SD₁₆	C₂×C₅	semidirect
138. C₃×C₄×SD₁₆	C₂×C₅	semidirect
139. C₃×#433	C₂×C₅	semidirect
183. #3125	C₃×C₅	direct (N × H)
313. #542	C₂×C₃×C₅	semidirect
314. #520	C₂×C₃×C₅	semidirect
315. #483	C₂×C₃×C₅	semidirect
316. #481	C₂×C₃×C₅	semidirect
317. #476	C₂×C₃×C₅	semidirect
318. #475	C₂×C₃×C₅	semidirect
319. #464	C₂×C₃×C₅	semidirect
320. #463	C₂×C₃×C₅	semidirect
321. #452	C₂×C₃×C₅	semidirect
323. #442	C₂×C₃×C₅	semidirect
324. #441	C₂×C₃×C₅	semidirect
325. C₄×SD₁₆	C₂×C₃×C₅	semidirect
326. C₄×SD₁₆	C₂×C₃×C₅	semidirect
327. #433	C₂×C₃×C₅	semidirect
595. C₃×C₅	#3125	direct (N × H)
668. C₅	C₃×#3125	direct (N × H)
692. C₃	C₅×#3125	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×#542	2
C₃×C₅×#520	2
C₃×C₅×#483	2
C₃×C₅×#481	2
C₃×C₅×#476	2
C₃×C₅×#475	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₃×C₅×#442	2
C₃×C₅×#441	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#433	2
C₅×#3125	3
C₃×#3125	5

Subgroups — C3×C5×#3125 #14276159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3125 #14276159