Subgroups — C₃×C₅×#3186 #14276220

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#480	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#466	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#447	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#3186	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	—	2	2	no	—
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
12	C₃×C₅×#121	—	2	2	no	—
13	C₃×C₅×#121	—	2	2	no	—
14	C₃×C₅×#121	C₂²	1	4	yes	—
15	C₃×C₅×#121	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
18	C₃×C₅×#107	C₂²	1	4	yes	complemented
19	C₃×C₅×#102	C₂²	1	8	yes	complemented
20	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
21	C₃×#3186	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
23	C₅×#480	C₂×C₃	1	4	yes	complemented
24	C₅×#466	C₂×C₃	1	4	yes	complemented
25	C₅×#447	C₂×C₃	1	4	yes	complemented
26	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃×C₅	—	2	2	no	—
28	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
29	C₂×C₃×C₅×D₄	—	2	4	no	—
30	C₂×C₃×C₅×D₄	—	2	4	no	—
31	C₂×C₃×C₅×D₄	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	4	4	no	—
33	C₂×C₃×C₅×D₄	—	4	8	no	—
34	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	—	4	2	no	—
37	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×D₈	—	4	4	no	—
42	C₂×C₃×C₅×C₈	—	4	2	no	—
43	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
46	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
49	C₃×#480	C₂×C₅	1	4	yes	complemented
50	C₃×#466	C₂×C₅	1	4	yes	complemented
51	C₃×#447	C₂×C₅	1	4	yes	complemented
52	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂²×C₅×D₄	—	2	2	no	—
54	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
55	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
57	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
58	C₅×#121	—	2	2	no	—
59	C₅×#121	—	2	2	no	—
60	C₅×#121	C₂²×C₃	1	4	yes	—
61	C₅×#121	C₂²×C₃	1	4	yes	complemented
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₅×#107	C₂²×C₃	1	4	yes	complemented
65	C₅×#102	C₂²×C₃	1	8	yes	complemented
66	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
67	#3186	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₂³×C₃×C₅	—	2	4	no	—
69	C₂³×C₃×C₅	—	4	1	no	—
70	C₂³×C₃×C₅	—	4	1	no	—
71	C₂³×C₃×C₅	—	4	4	no	—
72	C₂³×C₃×C₅	—	4	4	no	—
73	C₂³×C₃×C₅	—	4	4	no	—
74	C₂³×C₃×C₅	D₈	1	4	yes	complemented
75	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
76	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
77	C₃×C₅×D₄	—	2	8	no	—
78	C₃×C₅×D₄	—	4	4	no	—
79	C₃×C₅×D₄	—	4	8	no	—
80	C₃×C₅×D₄	—	4	8	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	4	2	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	4	4	no	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
90	C₃×C₅×C₈	—	2	4	no	—
91	C₂²×C₃×D₄	—	2	2	no	—
92	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
93	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
95	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
96	C₃×#121	—	2	2	no	—
97	C₃×#121	—	2	2	no	—
98	C₃×#121	C₂²×C₅	1	4	yes	—
99	C₃×#121	C₂²×C₅	1	4	yes	complemented
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
101	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
102	C₃×#107	C₂²×C₅	1	4	yes	complemented
103	C₃×#102	C₂²×C₅	1	8	yes	complemented
104	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
105	C₂⁴×C₅	—	2	2	no	—
106	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
107	C₂×C₅×D₄	—	2	4	no	—
108	C₂×C₅×D₄	—	2	4	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	4	4	no	—
111	C₂×C₅×D₄	—	4	8	no	—
112	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	4	2	no	—
115	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
116	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
118	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
119	C₅×D₈	—	4	4	no	—
120	C₂×C₅×C₈	—	4	2	no	—
121	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
124	C₅×C₂²⋊C₄	—	2	4	no	—
125	C₅×C₂²⋊C₄	—	2	4	no	—
126	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
127	#480	C₂×C₃×C₅	1	4	yes	complemented
128	#466	C₂×C₃×C₅	1	4	yes	complemented
129	#447	C₂×C₃×C₅	1	4	yes	complemented
130	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
131	C₂²×C₃×C₅	—	2	2	no	—
132	C₂²×C₃×C₅	—	2	1	no	—
133	C₂²×C₃×C₅	—	2	2	no	—
134	C₂²×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×C₅	—	4	4	no	—
136	C₂²×C₃×C₅	—	4	4	no	—
137	C₂²×C₃×C₅	—	4	4	no	—
138	C₂²×C₃×C₅	—	4	4	no	—
139	C₂²×C₃×C₅	—	8	8	no	—
140	C₂²×C₃×C₅	C₂×D₈	1	4	yes	—
141	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
142	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	—	2	2	no	—
145	C₃×C₄×C₅	—	4	4	no	—
146	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
147	C₂⁴×C₃	—	2	2	no	—
148	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
149	C₂×C₃×D₄	—	2	4	no	—
150	C₂×C₃×D₄	—	2	4	no	—
151	C₂×C₃×D₄	—	2	2	no	—
152	C₂×C₃×D₄	—	4	4	no	—
153	C₂×C₃×D₄	—	4	8	no	—
154	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	—	4	2	no	—
157	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
158	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
161	C₃×D₈	—	4	4	no	—
162	C₂×C₃×C₈	—	4	2	no	—
163	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
164	C₃×C₄⋊C₄	—	2	2	no	—
165	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
166	C₃×C₂²⋊C₄	—	2	4	no	—
167	C₃×C₂²⋊C₄	—	2	4	no	—
168	C₂³×C₅	—	2	4	no	—
169	C₂³×C₅	—	4	1	no	—
170	C₂³×C₅	—	4	1	no	—
171	C₂³×C₅	—	4	4	no	—
172	C₂³×C₅	—	4	4	no	—
173	C₂³×C₅	—	4	4	no	—
174	C₂³×C₅	C₃×D₈	1	4	yes	complemented
175	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
176	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
177	C₅×D₄	—	2	8	no	—
178	C₅×D₄	—	4	4	no	—
179	C₅×D₄	—	4	8	no	—
180	C₅×D₄	—	4	8	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	4	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	4	2	no	—
185	C₂×C₄×C₅	—	4	1	no	—
186	C₂×C₄×C₅	—	4	4	no	—
187	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
189	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
190	C₅×C₈	—	2	4	no	—
191	C₂²×D₄	—	2	2	no	—
192	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
193	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
194	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
195	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
196	#121	—	2	2	no	—
197	#121	—	2	2	no	—
198	#121	C₂²×C₃×C₅	1	4	yes	—
199	#121	C₂²×C₃×C₅	1	4	yes	complemented
200	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
201	C₂×C₂²⋊C₄	—	2	2	no	—
202	#107	C₂²×C₃×C₅	1	4	yes	complemented
203	#102	C₂²×C₃×C₅	1	8	yes	complemented
204	C₂²⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
205	C₂×C₃×C₅	—	2	4	no	—
206	C₂×C₃×C₅	—	2	2	no	—
207	C₂×C₃×C₅	—	8	4	no	—
208	C₂×C₃×C₅	#534	1	1	yes	characteristic
209	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
210	C₂×C₃×C₅	#575	1	1	yes	characteristic
211	C₂³×C₃	—	2	4	no	—
212	C₂³×C₃	—	4	1	no	—
213	C₂³×C₃	—	4	1	no	—
214	C₂³×C₃	—	4	4	no	—
215	C₂³×C₃	—	4	4	no	—
216	C₂³×C₃	—	4	4	no	—
217	C₂³×C₃	C₅×D₈	1	4	yes	complemented
218	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
219	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
220	C₃×D₄	—	2	8	no	—
221	C₃×D₄	—	4	4	no	—
222	C₃×D₄	—	4	8	no	—
223	C₃×D₄	—	4	8	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	4	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	4	2	no	—
228	C₂×C₃×C₄	—	4	1	no	—
229	C₂×C₃×C₄	—	4	4	no	—
230	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
232	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
233	C₃×C₈	—	2	4	no	—
234	C₂²×C₅	—	2	2	no	—
235	C₂²×C₅	—	2	1	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	2	1	no	—
238	C₂²×C₅	—	4	4	no	—
239	C₂²×C₅	—	4	4	no	—
240	C₂²×C₅	—	4	4	no	—
241	C₂²×C₅	—	4	4	no	—
242	C₂²×C₅	—	8	8	no	—
243	C₂²×C₅	C₂×C₃×D₈	1	4	yes	—
244	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
245	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
246	C₄×C₅	—	2	1	no	—
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	4	4	no	—
249	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
250	C₂⁴	—	2	2	no	—
251	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	4	4	no	—
256	C₂×D₄	—	4	8	no	—
257	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
261	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
262	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
263	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
264	D₈	—	4	4	no	—
265	C₂×C₈	—	4	2	no	—
266	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
267	C₄⋊C₄	—	2	2	no	—
268	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
269	C₂²⋊C₄	—	2	4	no	—
270	C₂²⋊C₄	—	2	4	no	—
271	C₃×C₅	#3186	1	1	yes	characteristic, direct product factor, Hall
272	C₂²×C₃	—	2	2	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	4	4	no	—
277	C₂²×C₃	—	4	4	no	—
278	C₂²×C₃	—	4	4	no	—
279	C₂²×C₃	—	4	4	no	—
280	C₂²×C₃	—	8	8	no	—
281	C₂²×C₃	C₂×C₅×D₈	1	4	yes	—
282	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
283	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
284	C₃×C₄	—	2	1	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	4	4	no	—
287	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
288	C₂×C₅	—	2	4	no	—
289	C₂×C₅	—	2	2	no	—
290	C₂×C₅	—	8	4	no	—
291	C₂×C₅	C₃×#534	1	1	yes	characteristic
292	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
293	C₂×C₅	C₃×#575	1	1	yes	characteristic
294	C₂³	—	2	4	no	—
295	C₂³	—	4	1	no	—
296	C₂³	—	4	1	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	4	4	no	—
299	C₂³	—	4	4	no	—
300	C₂³	C₃×C₅×D₈	1	4	yes	complemented
301	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
302	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
303	D₄	—	2	8	no	—
304	D₄	—	4	4	no	—
305	D₄	—	4	8	no	—
306	D₄	—	4	8	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
314	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
315	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
316	C₈	—	2	4	no	—
317	C₂×C₃	—	2	4	no	—
318	C₂×C₃	—	2	2	no	—
319	C₂×C₃	—	8	4	no	—
320	C₂×C₃	C₅×#534	1	1	yes	characteristic
321	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
322	C₂×C₃	C₅×#575	1	1	yes	characteristic
323	C₅	C₃×#3186	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²	—	2	2	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	4	4	no	—
329	C₂²	—	4	4	no	—
330	C₂²	—	4	4	no	—
331	C₂²	—	4	4	no	—
332	C₂²	—	8	8	no	—
333	C₂²	C₂×C₃×C₅×D₈	1	4	yes	—
334	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
335	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	1	no	—
338	C₄	—	4	4	no	—
339	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
340	C₃	C₅×#3186	1	1	yes	characteristic, direct product factor, Sylow
341	C₂	—	2	4	no	—
342	C₂	—	2	2	no	—
343	C₂	—	8	4	no	—
344	C₂	C₃×C₅×#534	1	1	yes	characteristic
345	C₂	C₂²×C₃×C₅×D₈	1	1	yes	characteristic
346	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₃×C₅×#480	C₂	semidirect
3. C₃×C₅×#466	C₂	semidirect
4. C₃×C₅×#447	C₂	semidirect
5. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
6. C₅×#3186	C₃	direct (N × H)
8. C₂²×C₃×C₅×D₄	C₂²	semidirect
10. C₂×C₃×C₅×D₈	C₂²	semidirect
11. C₂²×C₃×C₅×C₈	C₂²	semidirect
15. C₃×C₅×#121	C₂²	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
18. C₃×C₅×#107	C₂²	semidirect
19. C₃×C₅×#102	C₂²	semidirect
20. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
21. C₃×#3186	C₅	direct (N × H)
22. C₂×C₅×#121	C₂×C₃	semidirect
23. C₅×#480	C₂×C₃	semidirect
24. C₅×#466	C₂×C₃	semidirect
25. C₅×#447	C₂×C₃	semidirect
26. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
48. C₂×C₃×#121	C₂×C₅	semidirect
49. C₃×#480	C₂×C₅	semidirect
50. C₃×#466	C₂×C₅	semidirect
51. C₃×#447	C₂×C₅	semidirect
52. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
54. C₂²×C₅×D₄	C₂²×C₃	semidirect
56. C₂×C₅×D₈	C₂²×C₃	semidirect
57. C₂²×C₅×C₈	C₂²×C₃	semidirect
61. C₅×#121	C₂²×C₃	semidirect
62. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
64. C₅×#107	C₂²×C₃	semidirect
65. C₅×#102	C₂²×C₃	semidirect
66. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
67. #3186	C₃×C₅	direct (N × H)
74. C₂³×C₃×C₅	D₈	semidirect
92. C₂²×C₃×D₄	C₂²×C₅	semidirect
94. C₂×C₃×D₈	C₂²×C₅	semidirect
95. C₂²×C₃×C₈	C₂²×C₅	semidirect
99. C₃×#121	C₂²×C₅	semidirect
100. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
102. C₃×#107	C₂²×C₅	semidirect
103. C₃×#102	C₂²×C₅	semidirect
104. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
126. C₂×#121	C₂×C₃×C₅	semidirect
127. #480	C₂×C₃×C₅	semidirect
128. #466	C₂×C₃×C₅	semidirect
129. #447	C₂×C₃×C₅	semidirect
130. C₂×C₂²⋊C₈	C₂×C₃×C₅	semidirect
174. C₂³×C₅	C₃×D₈	semidirect
192. C₂²×D₄	C₂²×C₃×C₅	semidirect
194. C₂×D₈	C₂²×C₃×C₅	semidirect
195. C₂²×C₈	C₂²×C₃×C₅	semidirect
199. #121	C₂²×C₃×C₅	semidirect
200. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
202. #107	C₂²×C₃×C₅	semidirect
203. #102	C₂²×C₃×C₅	semidirect
204. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
217. C₂³×C₃	C₅×D₈	semidirect
271. C₃×C₅	#3186	direct (N × H)
300. C₂³	C₃×C₅×D₈	semidirect
323. C₅	C₃×#3186	direct (N × H)
340. C₃	C₅×#3186	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×#121	2
C₃×C₅×#480	2
C₃×C₅×#466	2
C₃×C₅×#447	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₅×#3186	3
C₃×#3186	5

Subgroups — C3×C5×#3186 #14276220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3186 #14276220