Subgroups — C₃×C₅×#3025 #14276059

Order 1920.

1532 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#525	C₂	1	3	yes	maximal, complemented
3	C₃×C₅×#458	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×B(4,𝔽₂)	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#410	C₂	1	3	yes	maximal, complemented
6	C₅×#3025	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×2₋¹⁺⁴	—	2	3	no	—
8	C₃×C₅×H(5,𝔽₂)	—	2	3	no	—
9	C₃×C₅×H(5,𝔽₂)	C₂²	1	4	yes	—
10	C₂×C₃×C₅×#41	—	2	6	no	—
11	C₂×C₃×C₅×#41	C₂²	1	3	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
13	C₃×C₅×#123	C₂²	1	6	yes	complemented
14	C₃×C₅×C₂²⋊Q₈	—	2	3	no	—
15	C₃×C₅×#121	—	2	3	no	—
16	C₃×C₅×#120	C₂²	1	6	yes	complemented
17	C₃×C₄×C₅×D₄	—	2	6	no	—
18	C₃×C₅×#117	C₂²	1	3	yes	complemented
19	C₃×C₅×#99	C₂²	1	12	yes	complemented
20	C₃×#3025	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₅×#585	C₂×C₃	1	1	yes	characteristic, complemented
22	C₅×#525	C₂×C₃	1	3	yes	complemented
23	C₅×#458	C₂×C₃	1	4	yes	complemented
24	C₅×B(4,𝔽₂)	C₂×C₃	1	4	yes	complemented
25	C₅×#410	C₂×C₃	1	3	yes	complemented
26	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
27	C₃×C₅×#41	—	2	4	no	—
28	C₃×C₅×#41	—	2	12	no	—
29	C₃×C₅×#41	—	2	6	no	—
30	C₃×C₅×#41	—	2	12	no	—
31	C₃×C₅×#41	—	2	6	no	—
32	C₂×C₃×C₅×Q₈	—	2	6	no	—
33	C₂×C₃×C₅×Q₈	D₄	1	3	yes	complemented
34	C₂×C₃×C₅×D₄	—	2	6	no	—
35	C₂×C₃×C₅×D₄	—	2	12	no	—
36	C₂×C₃×C₅×D₄	—	2	6	no	—
37	C₂×C₃×C₅×D₄	D₄	1	3	yes	complemented
38	C₂×C₃×C₅×D₄	C₂³	1	6	yes	—
39	C₂²×C₃×C₄×C₅	—	2	4	no	—
40	C₂²×C₃×C₄×C₅	—	2	3	no	—
41	C₂²×C₃×C₄×C₅	—	2	3	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	6	yes	complemented
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	—	2	3	no	—
46	C₃×C₅×C₄⋊C₄	—	2	6	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	6	no	—
49	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
50	C₃×C₄²×C₅	—	2	3	no	—
51	C₃×#585	C₂×C₅	1	1	yes	characteristic, complemented
52	C₃×#525	C₂×C₅	1	3	yes	complemented
53	C₃×#458	C₂×C₅	1	4	yes	complemented
54	C₃×B(4,𝔽₂)	C₂×C₅	1	4	yes	complemented
55	C₃×#410	C₂×C₅	1	3	yes	complemented
56	C₅×2₋¹⁺⁴	—	2	3	no	—
57	C₅×H(5,𝔽₂)	—	2	3	no	—
58	C₅×H(5,𝔽₂)	C₂²×C₃	1	4	yes	—
59	C₂×C₅×#41	—	2	6	no	—
60	C₂×C₅×#41	C₂²×C₃	1	3	yes	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
62	C₅×#123	C₂²×C₃	1	6	yes	complemented
63	C₅×C₂²⋊Q₈	—	2	3	no	—
64	C₅×#121	—	2	3	no	—
65	C₅×#120	C₂²×C₃	1	6	yes	complemented
66	C₄×C₅×D₄	—	2	6	no	—
67	C₅×#117	C₂²×C₃	1	3	yes	complemented
68	C₅×#99	C₂²×C₃	1	12	yes	complemented
69	#3025	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³×C₃×C₅	—	2	4	no	—
71	C₂³×C₃×C₅	—	2	3	no	—
72	C₂³×C₃×C₅	—	4	2	no	—
73	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
74	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
75	C₃×C₅×Q₈	—	2	4	no	—
76	C₃×C₅×Q₈	—	2	6	no	—
77	C₃×C₅×D₄	—	2	12	no	—
78	C₃×C₅×D₄	—	2	12	no	—
79	C₃×C₅×D₄	—	2	6	no	—
80	C₃×C₅×D₄	—	4	12	no	—
81	C₂×C₃×C₄×C₅	—	2	12	no	—
82	C₂×C₃×C₄×C₅	—	2	6	no	—
83	C₂×C₃×C₄×C₅	—	2	6	no	—
84	C₂×C₃×C₄×C₅	—	2	6	no	—
85	C₂×C₃×C₄×C₅	—	2	3	no	—
86	C₂×C₃×C₄×C₅	—	4	3	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
91	C₃×2₋¹⁺⁴	—	2	3	no	—
92	C₃×H(5,𝔽₂)	—	2	3	no	—
93	C₃×H(5,𝔽₂)	C₂²×C₅	1	4	yes	—
94	C₂×C₃×#41	—	2	6	no	—
95	C₂×C₃×#41	C₂²×C₅	1	3	yes	—
96	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
97	C₃×#123	C₂²×C₅	1	6	yes	complemented
98	C₃×C₂²⋊Q₈	—	2	3	no	—
99	C₃×#121	—	2	3	no	—
100	C₃×#120	C₂²×C₅	1	6	yes	complemented
101	C₃×C₄×D₄	—	2	6	no	—
102	C₃×#117	C₂²×C₅	1	3	yes	complemented
103	C₃×#99	C₂²×C₅	1	12	yes	complemented
104	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
105	C₅×#41	—	2	4	no	—
106	C₅×#41	—	2	12	no	—
107	C₅×#41	—	2	6	no	—
108	C₅×#41	—	2	12	no	—
109	C₅×#41	—	2	6	no	—
110	C₂×C₅×Q₈	—	2	6	no	—
111	C₂×C₅×Q₈	C₃×D₄	1	3	yes	complemented
112	C₂×C₅×D₄	—	2	6	no	—
113	C₂×C₅×D₄	—	2	12	no	—
114	C₂×C₅×D₄	—	2	6	no	—
115	C₂×C₅×D₄	C₃×D₄	1	3	yes	complemented
116	C₂×C₅×D₄	C₂³×C₃	1	6	yes	—
117	C₂²×C₄×C₅	—	2	4	no	—
118	C₂²×C₄×C₅	—	2	3	no	—
119	C₂²×C₄×C₅	—	2	3	no	—
120	C₂²×C₄×C₅	C₃×D₄	1	6	yes	complemented
121	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
123	C₅×C₄⋊C₄	—	2	3	no	—
124	C₅×C₄⋊C₄	—	2	6	no	—
125	C₅×C₂²⋊C₄	—	2	6	no	—
126	C₅×C₂²⋊C₄	—	2	6	no	—
127	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
128	C₄²×C₅	—	2	3	no	—
129	#585	C₂×C₃×C₅	1	1	yes	characteristic, complemented
130	#525	C₂×C₃×C₅	1	3	yes	complemented
131	#458	C₂×C₃×C₅	1	4	yes	complemented
132	B(4,𝔽₂)	C₂×C₃×C₅	1	4	yes	complemented
133	#410	C₂×C₃×C₅	1	3	yes	complemented
134	C₂²×C₃×C₅	—	2	6	no	—
135	C₂²×C₃×C₅	—	2	6	no	—
136	C₂²×C₃×C₅	—	4	1	no	—
137	C₂²×C₃×C₅	—	4	6	no	—
138	C₂²×C₃×C₅	—	4	3	no	—
139	C₂²×C₃×C₅	—	4	1	no	—
140	C₂²×C₃×C₅	—	8	4	no	—
141	C₂²×C₃×C₅	C₂²×D₄	1	3	yes	—
142	C₃×C₄×C₅	—	2	6	no	—
143	C₃×C₄×C₅	—	4	6	no	—
144	C₃×C₄×C₅	—	4	1	no	—
145	C₃×C₄×C₅	#120	1	3	yes	—
146	C₃×C₄×C₅	#120	1	1	yes	characteristic
147	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
148	C₃×#41	—	2	4	no	—
149	C₃×#41	—	2	12	no	—
150	C₃×#41	—	2	6	no	—
151	C₃×#41	—	2	12	no	—
152	C₃×#41	—	2	6	no	—
153	C₂×C₃×Q₈	—	2	6	no	—
154	C₂×C₃×Q₈	C₅×D₄	1	3	yes	complemented
155	C₂×C₃×D₄	—	2	6	no	—
156	C₂×C₃×D₄	—	2	12	no	—
157	C₂×C₃×D₄	—	2	6	no	—
158	C₂×C₃×D₄	C₅×D₄	1	3	yes	complemented
159	C₂×C₃×D₄	C₂³×C₅	1	6	yes	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	2	3	no	—
162	C₂²×C₃×C₄	—	2	3	no	—
163	C₂²×C₃×C₄	C₅×D₄	1	6	yes	complemented
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
166	C₃×C₄⋊C₄	—	2	3	no	—
167	C₃×C₄⋊C₄	—	2	6	no	—
168	C₃×C₂²⋊C₄	—	2	6	no	—
169	C₃×C₂²⋊C₄	—	2	6	no	—
170	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
171	C₃×C₄²	—	2	3	no	—
172	C₂³×C₅	—	2	4	no	—
173	C₂³×C₅	—	2	3	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
176	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
177	C₅×Q₈	—	2	4	no	—
178	C₅×Q₈	—	2	6	no	—
179	C₅×D₄	—	2	12	no	—
180	C₅×D₄	—	2	12	no	—
181	C₅×D₄	—	2	6	no	—
182	C₅×D₄	—	4	12	no	—
183	C₂×C₄×C₅	—	2	12	no	—
184	C₂×C₄×C₅	—	2	6	no	—
185	C₂×C₄×C₅	—	2	6	no	—
186	C₂×C₄×C₅	—	2	6	no	—
187	C₂×C₄×C₅	—	2	3	no	—
188	C₂×C₄×C₅	—	4	3	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
192	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
193	2₋¹⁺⁴	—	2	3	no	—
194	H(5,𝔽₂)	—	2	3	no	—
195	H(5,𝔽₂)	C₂²×C₃×C₅	1	4	yes	—
196	C₂×#41	—	2	6	no	—
197	C₂×#41	C₂²×C₃×C₅	1	3	yes	—
198	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
199	#123	C₂²×C₃×C₅	1	6	yes	complemented
200	C₂²⋊Q₈	—	2	3	no	—
201	#121	—	2	3	no	—
202	#120	C₂²×C₃×C₅	1	6	yes	complemented
203	C₄×D₄	—	2	6	no	—
204	#117	C₂²×C₃×C₅	1	3	yes	complemented
205	#99	C₂²×C₃×C₅	1	12	yes	complemented
206	C₂×C₃×C₅	—	2	3	no	—
207	C₂×C₃×C₅	—	4	2	no	—
208	C₂×C₃×C₅	—	4	6	no	—
209	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
210	C₂³×C₃	—	2	4	no	—
211	C₂³×C₃	—	2	3	no	—
212	C₂³×C₃	—	4	2	no	—
213	C₂³×C₃	C₂×C₅×D₄	1	6	yes	—
214	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
215	C₃×Q₈	—	2	4	no	—
216	C₃×Q₈	—	2	6	no	—
217	C₃×D₄	—	2	12	no	—
218	C₃×D₄	—	2	12	no	—
219	C₃×D₄	—	2	6	no	—
220	C₃×D₄	—	4	12	no	—
221	C₂×C₃×C₄	—	2	12	no	—
222	C₂×C₃×C₄	—	2	6	no	—
223	C₂×C₃×C₄	—	2	6	no	—
224	C₂×C₃×C₄	—	2	6	no	—
225	C₂×C₃×C₄	—	2	3	no	—
226	C₂×C₃×C₄	—	4	3	no	—
227	C₂×C₃×C₄	—	4	1	no	—
228	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
229	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
230	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
231	C₂²×C₅	—	2	6	no	—
232	C₂²×C₅	—	2	6	no	—
233	C₂²×C₅	—	4	1	no	—
234	C₂²×C₅	—	4	6	no	—
235	C₂²×C₅	—	4	3	no	—
236	C₂²×C₅	—	4	1	no	—
237	C₂²×C₅	—	8	4	no	—
238	C₂²×C₅	C₂²×C₃×D₄	1	3	yes	—
239	C₄×C₅	—	2	6	no	—
240	C₄×C₅	—	4	6	no	—
241	C₄×C₅	—	4	1	no	—
242	C₄×C₅	C₃×#120	1	3	yes	—
243	C₄×C₅	C₃×#120	1	1	yes	characteristic
244	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
245	#41	—	2	4	no	—
246	#41	—	2	12	no	—
247	#41	—	2	6	no	—
248	#41	—	2	12	no	—
249	#41	—	2	6	no	—
250	C₂×Q₈	—	2	6	no	—
251	C₂×Q₈	C₃×C₅×D₄	1	3	yes	complemented
252	C₂×D₄	—	2	6	no	—
253	C₂×D₄	—	2	12	no	—
254	C₂×D₄	—	2	6	no	—
255	C₂×D₄	C₃×C₅×D₄	1	3	yes	complemented
256	C₂×D₄	C₂³×C₃×C₅	1	6	yes	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	3	no	—
259	C₂²×C₄	—	2	3	no	—
260	C₂²×C₄	C₃×C₅×D₄	1	6	yes	complemented
261	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
263	C₄⋊C₄	—	2	3	no	—
264	C₄⋊C₄	—	2	6	no	—
265	C₂²⋊C₄	—	2	6	no	—
266	C₂²⋊C₄	—	2	6	no	—
267	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	—
268	C₄²	—	2	3	no	—
269	C₃×C₅	#3025	1	1	yes	characteristic, direct product factor, Hall
270	C₂²×C₃	—	2	6	no	—
271	C₂²×C₃	—	2	6	no	—
272	C₂²×C₃	—	4	1	no	—
273	C₂²×C₃	—	4	6	no	—
274	C₂²×C₃	—	4	3	no	—
275	C₂²×C₃	—	4	1	no	—
276	C₂²×C₃	—	8	4	no	—
277	C₂²×C₃	C₂²×C₅×D₄	1	3	yes	—
278	C₃×C₄	—	2	6	no	—
279	C₃×C₄	—	4	6	no	—
280	C₃×C₄	—	4	1	no	—
281	C₃×C₄	C₅×#120	1	3	yes	—
282	C₃×C₄	C₅×#120	1	1	yes	characteristic
283	C₂×C₅	—	2	3	no	—
284	C₂×C₅	—	4	2	no	—
285	C₂×C₅	—	4	6	no	—
286	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
287	C₂³	—	2	4	no	—
288	C₂³	—	2	3	no	—
289	C₂³	—	4	2	no	—
290	C₂³	C₂×C₃×C₅×D₄	1	6	yes	—
291	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
292	Q₈	—	2	4	no	—
293	Q₈	—	2	6	no	—
294	D₄	—	2	12	no	—
295	D₄	—	2	12	no	—
296	D₄	—	2	6	no	—
297	D₄	—	4	12	no	—
298	C₂×C₄	—	2	12	no	—
299	C₂×C₄	—	2	6	no	—
300	C₂×C₄	—	2	6	no	—
301	C₂×C₄	—	2	6	no	—
302	C₂×C₄	—	2	3	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	3	no	—
305	C₂×C₄	C₂×C₃×C₅×D₄	1	6	yes	—
306	C₂×C₄	C₂×C₃×C₅×D₄	1	3	yes	—
307	C₂×C₄	C₂×C₃×C₅×D₄	1	3	yes	—
308	C₂×C₃	—	2	3	no	—
309	C₂×C₃	—	4	2	no	—
310	C₂×C₃	—	4	6	no	—
311	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
312	C₅	C₃×#3025	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²	—	2	6	no	—
314	C₂²	—	2	6	no	—
315	C₂²	—	4	1	no	—
316	C₂²	—	4	6	no	—
317	C₂²	—	4	3	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	8	4	no	—
320	C₂²	C₂²×C₃×C₅×D₄	1	3	yes	—
321	C₄	—	2	6	no	—
322	C₄	—	4	6	no	—
323	C₄	—	4	1	no	—
324	C₄	C₃×C₅×#120	1	1	yes	characteristic
325	C₄	C₃×C₅×#120	1	3	yes	—
326	C₃	C₅×#3025	1	1	yes	characteristic, direct product factor, Sylow
327	C₂	—	2	3	no	—
328	C₂	—	4	2	no	—
329	C₂	—	4	6	no	—
330	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle	C₂×C₃×C₅	C₂×#120
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#585	C₂	semidirect
2. C₃×C₅×#525	C₂	semidirect
3. C₃×C₅×#458	C₂	semidirect
4. C₃×C₅×B(4,𝔽₂)	C₂	semidirect
5. C₃×C₅×#410	C₂	semidirect
6. C₅×#3025	C₃	direct (N × H)
12. C₂³×C₃×C₄×C₅	C₂²	semidirect
13. C₃×C₅×#123	C₂²	semidirect
16. C₃×C₅×#120	C₂²	semidirect
18. C₃×C₅×#117	C₂²	semidirect
19. C₃×C₅×#99	C₂²	semidirect
20. C₃×#3025	C₅	direct (N × H)
21. C₅×#585	C₂×C₃	semidirect
22. C₅×#525	C₂×C₃	semidirect
23. C₅×#458	C₂×C₃	semidirect
24. C₅×B(4,𝔽₂)	C₂×C₃	semidirect
25. C₅×#410	C₂×C₃	semidirect
33. C₂×C₃×C₅×Q₈	D₄	semidirect
37. C₂×C₃×C₅×D₄	D₄	semidirect
42. C₂²×C₃×C₄×C₅	D₄	semidirect
51. C₃×#585	C₂×C₅	semidirect
52. C₃×#525	C₂×C₅	semidirect
53. C₃×#458	C₂×C₅	semidirect
54. C₃×B(4,𝔽₂)	C₂×C₅	semidirect
55. C₃×#410	C₂×C₅	semidirect
61. C₂³×C₄×C₅	C₂²×C₃	semidirect
62. C₅×#123	C₂²×C₃	semidirect
65. C₅×#120	C₂²×C₃	semidirect
67. C₅×#117	C₂²×C₃	semidirect
68. C₅×#99	C₂²×C₃	semidirect
69. #3025	C₃×C₅	direct (N × H)
96. C₂³×C₃×C₄	C₂²×C₅	semidirect
97. C₃×#123	C₂²×C₅	semidirect
100. C₃×#120	C₂²×C₅	semidirect
102. C₃×#117	C₂²×C₅	semidirect
103. C₃×#99	C₂²×C₅	semidirect
111. C₂×C₅×Q₈	C₃×D₄	semidirect
115. C₂×C₅×D₄	C₃×D₄	semidirect
120. C₂²×C₄×C₅	C₃×D₄	semidirect
129. #585	C₂×C₃×C₅	semidirect
130. #525	C₂×C₃×C₅	semidirect
131. #458	C₂×C₃×C₅	semidirect
132. B(4,𝔽₂)	C₂×C₃×C₅	semidirect
133. #410	C₂×C₃×C₅	semidirect
154. C₂×C₃×Q₈	C₅×D₄	semidirect
158. C₂×C₃×D₄	C₅×D₄	semidirect
163. C₂²×C₃×C₄	C₅×D₄	semidirect
198. C₂³×C₄	C₂²×C₃×C₅	semidirect
199. #123	C₂²×C₃×C₅	semidirect
202. #120	C₂²×C₃×C₅	semidirect
204. #117	C₂²×C₃×C₅	semidirect
205. #99	C₂²×C₃×C₅	semidirect
251. C₂×Q₈	C₃×C₅×D₄	semidirect
255. C₂×D₄	C₃×C₅×D₄	semidirect
260. C₂²×C₄	C₃×C₅×D₄	semidirect
269. C₃×C₅	#3025	direct (N × H)
312. C₅	C₃×#3025	direct (N × H)
326. C₃	C₅×#3025	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×#585	2
C₃×C₅×#525	2
C₃×C₅×#458	2
C₃×C₅×B(4,𝔽₂)	2
C₃×C₅×#410	2
C₅×#3025	3
C₃×#3025	5

Subgroups — C3×C5×#3025 #14276059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3025 #14276059