Subgroups — C₃×C₅×#553 #11756642

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#126	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#123	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#553	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	—
20	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	—
21	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₃×C₄²×C₅	C₂²	1	2	yes	—
35	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₃×#553	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#126	C₂×C₃	1	2	yes	complemented
38	C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#123	C₂×C₃	1	2	yes	complemented
40	C₅×#121	C₂×C₃	1	2	yes	complemented
41	C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
43	C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
45	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
49	C₂³×C₃×C₅	C₂³	1	2	yes	—
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₃×C₅×D₄	—	2	4	no	—
52	C₃×C₅×D₄	—	2	2	no	—
53	C₃×C₅×D₄	—	2	2	no	—
54	C₃×C₅×D₄	—	4	2	no	—
55	C₂×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₄×C₅	—	2	2	no	—
57	C₂×C₃×C₄×C₅	—	4	2	no	—
58	C₂×C₃×C₄×C₅	—	4	2	no	—
59	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₃×#126	C₂×C₅	1	2	yes	complemented
68	C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#123	C₂×C₅	1	2	yes	complemented
70	C₃×#121	C₂×C₅	1	2	yes	complemented
71	C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
74	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
76	C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×C₅×D₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×D₄	C₂²×C₃	1	2	yes	—
82	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	—
85	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	—
86	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₄²×C₅	C₂²×C₃	1	2	yes	—
100	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
101	#553	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
102	C₂²×C₃×C₅	—	2	1	no	—
103	C₂²×C₃×C₅	—	2	1	no	—
104	C₂²×C₃×C₅	—	2	1	no	—
105	C₂²×C₃×C₅	—	2	1	no	—
106	C₂²×C₃×C₅	—	2	2	no	—
107	C₂²×C₃×C₅	—	2	2	no	—
108	C₂²×C₃×C₅	—	2	2	no	—
109	C₂²×C₃×C₅	—	2	1	no	—
110	C₂²×C₃×C₅	#41	1	2	yes	—
111	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₄×C₅	—	2	1	no	—
113	C₃×C₄×C₅	—	2	1	no	—
114	C₃×C₄×C₅	—	2	2	no	—
115	C₃×C₄×C₅	—	2	1	no	—
116	C₃×C₄×C₅	—	2	1	no	—
117	C₃×C₄×C₅	—	2	2	no	—
118	C₃×C₄×C₅	—	2	2	no	—
119	C₃×C₄×C₅	#41	1	2	yes	—
120	C₂×C₃×D₄	C₂²×C₅	1	2	yes	—
121	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×D₄	C₂²×C₅	1	2	yes	—
124	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	—
127	C₂²×C₃×C₄	C₂²×C₅	1	2	yes	—
128	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
131	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
132	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
133	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
135	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
136	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
138	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
139	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
140	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
141	C₃×C₄²	C₂²×C₅	1	2	yes	—
142	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
143	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₂³×C₅	C₂³×C₃	1	2	yes	—
145	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₅×D₄	—	2	4	no	—
147	C₅×D₄	—	2	2	no	—
148	C₅×D₄	—	2	2	no	—
149	C₅×D₄	—	4	2	no	—
150	C₂×C₄×C₅	—	2	2	no	—
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	4	2	no	—
153	C₂×C₄×C₅	—	4	2	no	—
154	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
156	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
158	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	#126	C₂×C₃×C₅	1	2	yes	complemented
163	#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
164	#123	C₂×C₃×C₅	1	2	yes	complemented
165	#121	C₂×C₃×C₅	1	2	yes	complemented
166	#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
168	C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
169	C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
170	C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
171	#117	C₂×C₃×C₅	1	1	yes	characteristic, complemented
172	C₂×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
173	C₂×C₃×C₅	—	2	2	no	—
174	C₂×C₃×C₅	—	4	1	no	—
175	C₂×C₃×C₅	—	4	2	no	—
176	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
177	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
178	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
180	C₂³×C₃	C₂³×C₅	1	2	yes	—
181	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
182	C₃×D₄	—	2	4	no	—
183	C₃×D₄	—	2	2	no	—
184	C₃×D₄	—	2	2	no	—
185	C₃×D₄	—	4	2	no	—
186	C₂×C₃×C₄	—	2	2	no	—
187	C₂×C₃×C₄	—	2	2	no	—
188	C₂×C₃×C₄	—	4	2	no	—
189	C₂×C₃×C₄	—	4	2	no	—
190	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
191	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
192	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
194	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
195	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
197	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂²×C₅	—	2	1	no	—
199	C₂²×C₅	—	2	1	no	—
200	C₂²×C₅	—	2	1	no	—
201	C₂²×C₅	—	2	1	no	—
202	C₂²×C₅	—	2	2	no	—
203	C₂²×C₅	—	2	2	no	—
204	C₂²×C₅	—	2	2	no	—
205	C₂²×C₅	—	2	1	no	—
206	C₂²×C₅	C₃×#41	1	2	yes	—
207	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
208	C₄×C₅	—	2	1	no	—
209	C₄×C₅	—	2	1	no	—
210	C₄×C₅	—	2	2	no	—
211	C₄×C₅	—	2	1	no	—
212	C₄×C₅	—	2	1	no	—
213	C₄×C₅	—	2	2	no	—
214	C₄×C₅	—	2	2	no	—
215	C₄×C₅	C₃×#41	1	2	yes	—
216	C₂×D₄	C₂²×C₃×C₅	1	2	yes	—
217	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂×D₄	C₂²×C₃×C₅	1	2	yes	—
220	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
221	C₂²×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
222	C₂²×C₄	C₂²×C₃×C₅	1	2	yes	—
223	C₂²×C₄	C₂²×C₃×C₅	1	2	yes	—
224	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
226	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
227	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
229	C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
231	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
232	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
233	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
234	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
235	C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
236	C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
237	C₄²	C₂²×C₃×C₅	1	2	yes	—
238	C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
239	C₃×C₅	#553	1	1	yes	characteristic, direct product factor, Hall
240	C₂²×C₃	—	2	1	no	—
241	C₂²×C₃	—	2	1	no	—
242	C₂²×C₃	—	2	1	no	—
243	C₂²×C₃	—	2	1	no	—
244	C₂²×C₃	—	2	2	no	—
245	C₂²×C₃	—	2	2	no	—
246	C₂²×C₃	—	2	2	no	—
247	C₂²×C₃	—	2	1	no	—
248	C₂²×C₃	C₅×#41	1	2	yes	—
249	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
250	C₃×C₄	—	2	1	no	—
251	C₃×C₄	—	2	1	no	—
252	C₃×C₄	—	2	2	no	—
253	C₃×C₄	—	2	1	no	—
254	C₃×C₄	—	2	1	no	—
255	C₃×C₄	—	2	2	no	—
256	C₃×C₄	—	2	2	no	—
257	C₃×C₄	C₅×#41	1	2	yes	—
258	C₂×C₅	—	2	2	no	—
259	C₂×C₅	—	4	1	no	—
260	C₂×C₅	—	4	2	no	—
261	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
262	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
263	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
264	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
265	C₂³	C₂³×C₃×C₅	1	2	yes	—
266	C₂³	C₂³×C₃×C₅	1	1	yes	characteristic
267	D₄	—	2	4	no	—
268	D₄	—	2	2	no	—
269	D₄	—	2	2	no	—
270	D₄	—	4	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
276	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
277	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
278	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
279	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
280	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
281	C₂×C₄	C₂³×C₃×C₅	1	2	yes	—
282	C₂×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
283	C₂×C₃	—	2	2	no	—
284	C₂×C₃	—	4	1	no	—
285	C₂×C₃	—	4	2	no	—
286	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
287	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
288	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
289	C₅	C₃×#553	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²	—	2	1	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	2	1	no	—
293	C₂²	—	2	1	no	—
294	C₂²	—	2	2	no	—
295	C₂²	—	2	2	no	—
296	C₂²	—	2	2	no	—
297	C₂²	—	2	1	no	—
298	C₂²	C₃×C₅×#41	1	2	yes	—
299	C₂²	C₂⁴×C₃×C₅	1	1	yes	characteristic
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	2	no	—
303	C₄	—	2	1	no	—
304	C₄	—	2	1	no	—
305	C₄	—	2	2	no	—
306	C₄	—	2	2	no	—
307	C₄	C₃×C₅×#41	1	2	yes	—
308	C₃	C₅×#553	1	1	yes	characteristic, direct product factor, Sylow
309	C₂	—	2	2	no	—
310	C₂	—	4	1	no	—
311	C₂	—	4	2	no	—
312	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
313	C₂	C₂×C₃×C₅×#41	1	1	yes	characteristic
314	C₂	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#126	C₂	semidirect
2. C₃×C₅×#125	C₂	semidirect
3. C₃×C₅×#123	C₂	semidirect
4. C₃×C₅×#121	C₂	semidirect
5. C₃×C₅×#121	C₂	semidirect
6. C₃×C₅×#121	C₂	semidirect
7. C₃×C₄×C₅×D₄	C₂	semidirect
8. C₃×C₄×C₅×D₄	C₂	semidirect
9. C₃×C₄×C₅×D₄	C₂	semidirect
10. C₃×C₅×#117	C₂	semidirect
11. C₂×C₃×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#553	C₃	direct (N × H)
36. C₃×#553	C₅	direct (N × H)
37. C₅×#126	C₂×C₃	semidirect
38. C₅×#125	C₂×C₃	semidirect
39. C₅×#123	C₂×C₃	semidirect
40. C₅×#121	C₂×C₃	semidirect
41. C₅×#121	C₂×C₃	semidirect
42. C₅×#121	C₂×C₃	semidirect
43. C₄×C₅×D₄	C₂×C₃	semidirect
44. C₄×C₅×D₄	C₂×C₃	semidirect
45. C₄×C₅×D₄	C₂×C₃	semidirect
46. C₅×#117	C₂×C₃	semidirect
47. C₂×C₅×C₄⋊C₄	C₂×C₃	semidirect
67. C₃×#126	C₂×C₅	semidirect
68. C₃×#125	C₂×C₅	semidirect
69. C₃×#123	C₂×C₅	semidirect
70. C₃×#121	C₂×C₅	semidirect
71. C₃×#121	C₂×C₅	semidirect
72. C₃×#121	C₂×C₅	semidirect
73. C₃×C₄×D₄	C₂×C₅	semidirect
74. C₃×C₄×D₄	C₂×C₅	semidirect
75. C₃×C₄×D₄	C₂×C₅	semidirect
76. C₃×#117	C₂×C₅	semidirect
77. C₂×C₃×C₄⋊C₄	C₂×C₅	semidirect
101. #553	C₃×C₅	direct (N × H)
162. #126	C₂×C₃×C₅	semidirect
163. #125	C₂×C₃×C₅	semidirect
164. #123	C₂×C₃×C₅	semidirect
165. #121	C₂×C₃×C₅	semidirect
166. #121	C₂×C₃×C₅	semidirect
167. #121	C₂×C₃×C₅	semidirect
168. C₄×D₄	C₂×C₃×C₅	semidirect
169. C₄×D₄	C₂×C₃×C₅	semidirect
170. C₄×D₄	C₂×C₃×C₅	semidirect
171. #117	C₂×C₃×C₅	semidirect
172. C₂×C₄⋊C₄	C₂×C₃×C₅	semidirect
239. C₃×C₅	#553	direct (N × H)
289. C₅	C₃×#553	direct (N × H)
308. C₃	C₅×#553	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×#126	2
C₃×C₅×#125	2
C₃×C₅×#123	2
C₃×C₅×#121	2
C₃×C₄×C₅×D₄	2
C₃×C₅×#117	2
C₂×C₃×C₅×C₄⋊C₄	2
C₅×#553	3
C₃×#553	5

Subgroups — C3×C5×#553 #11756642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#553 #11756642