Subgroups — C₃×#10613955 #14320148

Order 1920.

1312 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×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#65266	C₂	1	2	yes	maximal, complemented
5	C₃×#65265	C₂	1	2	yes	maximal, complemented
6	C₃×#65231	C₂	1	4	yes	maximal
7	C₃×C₄×#683	C₂	1	4	yes	maximal, complemented
8	#10613955	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
11	C₃×C₅×#117	—	2	4	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
16	C₃×#4072	—	2	4	no	—
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×#683	C₂²	1	8	yes	—
19	C₂×C₃×C₄×Dic₅	C₄	1	8	yes	complemented
20	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₃×#3963	C₂²	1	8	yes	—
25	C₃×#2285	—	5	1	no	maximal, Hall
26	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
27	C₂×#4072	C₂×C₃	1	1	yes	characteristic
28	C₂²×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
29	#65266	C₂×C₃	1	2	yes	complemented
30	#65265	C₂×C₃	1	2	yes	complemented
31	#65231	C₂×C₃	1	4	yes	—
32	C₄×#683	C₂×C₃	1	4	yes	complemented
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
36	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₅	—	2	8	no	—
41	C₂²×C₃×Dic₅	C₂×C₄	1	8	yes	—
42	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
43	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
47	C₃×C₄²×C₅	—	2	4	no	—
48	C₃×C₂²⋊Dic₅	—	2	4	no	—
49	C₃×C₄⋊Dic₅	—	2	4	no	—
50	C₃×#683	—	2	16	no	—
51	C₃×C₄×Dic₅	—	2	4	no	—
52	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
53	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	—
54	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
55	C₂×C₃×#117	—	5	1	no	—
56	C₂×C₃×#117	D₅	1	1	yes	characteristic
57	C₂²×C₃×C₄²	—	5	1	no	—
58	C₃×#384	—	5	2	no	—
59	C₃×#382	—	5	2	no	—
60	C₃×#380	—	5	4	no	—
61	C₃×C₄×C₄⋊C₄	—	5	4	no	—
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
64	C₅×#117	—	2	4	no	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
68	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
69	#4072	—	2	4	no	—
70	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
71	C₂×#683	C₂²×C₃	1	8	yes	—
72	C₂×C₄×Dic₅	C₃×C₄	1	8	yes	complemented
73	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
74	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
75	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
77	#3963	C₂²×C₃	1	8	yes	—
78	#2285	—	5	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
83	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	8	no	—
86	C₂×C₃×C₄×C₅	C₄⋊C₄	1	16	yes	complemented
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
93	C₂×C₃×Dic₅	—	2	4	no	—
94	C₂×C₃×Dic₅	—	2	16	no	—
95	C₂×C₃×Dic₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	8	no	—
97	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
98	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
99	C₂×C₃×Dic₅	#41	1	8	yes	—
100	C₂³×C₃×C₄	—	5	2	no	—
101	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
102	C₃×#117	—	2	4	no	—
103	C₃×#117	—	10	4	no	—
104	C₂×C₃×C₄⋊C₄	—	5	8	no	—
105	C₂×C₃×C₄⋊C₄	—	5	2	no	—
106	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
107	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
108	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
109	C₂×C₃×C₄²	—	5	8	no	—
110	C₂×C₃×C₄²	—	5	1	no	—
111	C₂×C₃×C₄²	—	5	1	no	—
112	C₂×C₃×C₄²	—	5	2	no	—
113	C₂×C₃×C₄²	—	5	2	no	—
114	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
115	C₃×#95	—	5	8	no	—
116	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
118	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
119	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
123	C₂²×Dic₅	—	2	8	no	—
124	C₂²×Dic₅	C₂×C₃×C₄	1	8	yes	—
125	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
126	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
127	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₂²⋊C₄	—	2	4	no	—
130	C₄²×C₅	—	2	4	no	—
131	C₂²⋊Dic₅	—	2	4	no	—
132	C₄⋊Dic₅	—	2	4	no	—
133	#683	—	2	16	no	—
134	C₄×Dic₅	—	2	4	no	—
135	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
136	C₄×Dic₅	C₂×C₃×C₄	1	8	yes	—
137	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
138	C₂×#117	—	5	1	no	—
139	C₂×#117	C₃×D₅	1	1	yes	characteristic
140	C₂²×C₄²	—	5	1	no	—
141	#384	—	5	2	no	—
142	#382	—	5	2	no	—
143	#380	—	5	4	no	—
144	C₄×C₄⋊C₄	—	5	4	no	—
145	C₂²×C₃×C₅	—	2	4	no	—
146	C₂²×C₃×C₅	—	2	4	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
149	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
153	C₃×C₄×C₅	—	4	4	no	—
154	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
155	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
156	C₃×Dic₅	—	2	4	no	—
157	C₃×Dic₅	—	4	4	no	—
158	C₃×Dic₅	#117	1	8	yes	complemented
159	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	—	5	2	no	—
161	C₂²×C₃×C₄	—	5	8	no	—
162	C₂²×C₃×C₄	—	5	2	no	—
163	C₂²×C₃×C₄	—	5	4	no	—
164	C₂²×C₃×C₄	—	10	8	no	—
165	C₂²×C₃×C₄	Dic₁₀	1	4	yes	—
166	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
167	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
168	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
169	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₄⋊C₄	—	10	16	no	—
173	C₃×C₄⋊C₄	—	10	4	no	—
174	C₃×C₂²⋊C₄	—	2	4	no	—
175	C₃×C₂²⋊C₄	—	10	4	no	—
176	C₃×C₄²	—	2	4	no	—
177	C₃×C₄²	—	5	4	no	—
178	C₃×C₄²	—	5	8	no	—
179	C₃×C₄²	—	5	4	no	—
180	C₃×C₄²	—	10	4	no	—
181	C₂³×C₅	—	2	4	no	—
182	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
183	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
184	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
185	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	8	no	—
188	C₂×C₄×C₅	C₃×C₄⋊C₄	1	16	yes	complemented
189	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
190	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
192	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
193	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
194	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
195	C₂×Dic₅	—	2	4	no	—
196	C₂×Dic₅	—	2	16	no	—
197	C₂×Dic₅	—	2	4	no	—
198	C₂×Dic₅	—	2	8	no	—
199	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
200	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
201	C₂×Dic₅	C₃×#41	1	8	yes	—
202	C₂³×C₄	—	5	2	no	—
203	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
204	#117	—	2	4	no	—
205	#117	—	10	4	no	—
206	C₂×C₄⋊C₄	—	5	2	no	—
207	C₂×C₄⋊C₄	—	5	8	no	—
208	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
209	C₂×C₂²⋊C₄	—	5	2	no	—
210	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
211	C₂×C₄²	—	5	8	no	—
212	C₂×C₄²	—	5	2	no	—
213	C₂×C₄²	—	5	1	no	—
214	C₂×C₄²	—	5	1	no	—
215	C₂×C₄²	—	5	2	no	—
216	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
217	#95	—	5	8	no	—
218	C₂×C₃×C₅	—	2	4	no	—
219	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₃×C₅	C₂×#117	1	2	yes	—
221	C₂×C₃×C₅	#532	1	2	yes	—
222	C₂×C₃×C₅	#533	1	2	yes	—
223	C₂³×C₃	—	2	4	no	—
224	C₂³×C₃	C₂×Dic₁₀	1	2	yes	—
225	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
226	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
227	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
228	C₂×C₃×C₄	—	2	8	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	5	4	no	—
231	C₂×C₃×C₄	—	5	8	no	—
232	C₂×C₃×C₄	—	5	4	no	—
233	C₂×C₃×C₄	—	10	16	no	—
234	C₂×C₃×C₄	—	10	4	no	—
235	C₂×C₃×C₄	—	10	8	no	—
236	C₂×C₃×C₄	—	10	4	no	—
237	C₂×C₃×C₄	#683	1	16	yes	complemented
238	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
239	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
240	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
241	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
242	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
243	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
244	C₂²×C₅	—	2	4	no	—
245	C₂²×C₅	—	2	4	no	—
246	C₂²×C₅	—	2	4	no	—
247	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
248	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
249	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
250	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
251	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
252	C₄×C₅	—	4	4	no	—
253	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
254	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
255	Dic₅	—	2	4	no	—
256	Dic₅	—	4	4	no	—
257	Dic₅	C₃×#117	1	8	yes	complemented
258	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
259	C₂²×C₄	—	5	2	no	—
260	C₂²×C₄	—	5	8	no	—
261	C₂²×C₄	—	5	2	no	—
262	C₂²×C₄	—	5	4	no	—
263	C₂²×C₄	—	10	8	no	—
264	C₂²×C₄	C₃×Dic₁₀	1	4	yes	—
265	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
266	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
267	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
268	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	10	16	no	—
272	C₄⋊C₄	—	10	4	no	—
273	C₂²⋊C₄	—	2	4	no	—
274	C₂²⋊C₄	—	10	4	no	—
275	C₄²	—	2	4	no	—
276	C₄²	—	5	4	no	—
277	C₄²	—	5	8	no	—
278	C₄²	—	5	4	no	—
279	C₄²	—	10	4	no	—
280	C₃×C₅	#2285	1	1	yes	characteristic, complemented, Hall
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	—	2	4	no	—
283	C₂²×C₃	—	2	4	no	—
284	C₂²×C₃	C₂×#683	1	4	yes	—
285	C₂²×C₃	C₂²×Dic₁₀	1	1	yes	characteristic
286	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
287	C₂²×C₃	D₅×#41	1	4	yes	—
288	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
289	C₃×C₄	—	4	4	no	—
290	C₃×C₄	—	5	8	no	—
291	C₃×C₄	—	10	4	no	—
292	C₃×C₄	—	20	4	no	—
293	C₃×C₄	C₂×#683	1	4	yes	—
294	C₃×C₄	C₂×#683	1	4	yes	—
295	C₂×C₅	—	2	4	no	—
296	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
297	C₂×C₅	C₂×C₃×#117	1	2	yes	—
298	C₂×C₅	C₃×#532	1	2	yes	—
299	C₂×C₅	C₃×#533	1	2	yes	—
300	C₂³	—	2	4	no	—
301	C₂³	C₂×C₃×Dic₁₀	1	2	yes	—
302	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
303	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
304	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	5	4	no	—
308	C₂×C₄	—	5	8	no	—
309	C₂×C₄	—	5	4	no	—
310	C₂×C₄	—	10	16	no	—
311	C₂×C₄	—	10	4	no	—
312	C₂×C₄	—	10	8	no	—
313	C₂×C₄	—	10	4	no	—
314	C₂×C₄	C₃×#683	1	16	yes	complemented
315	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
316	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
317	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
318	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
319	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
320	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
321	C₂×C₃	—	2	4	no	—
322	C₂×C₃	#65851	1	2	yes	—
323	C₂×C₃	D₅×#117	1	2	yes	—
324	C₂×C₃	C₂²×#683	1	1	yes	characteristic
325	C₂×C₃	#66166	1	2	yes	—
326	C₅	C₃×#2285	1	1	yes	characteristic, complemented, Sylow
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	C₂×C₃×#683	1	4	yes	—
331	C₂²	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
332	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
333	C₂²	C₃×D₅×#41	1	4	yes	—
334	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
335	C₄	—	4	4	no	—
336	C₄	—	5	8	no	—
337	C₄	—	10	4	no	—
338	C₄	—	20	4	no	—
339	C₄	C₂×C₃×#683	1	4	yes	—
340	C₄	C₂×C₃×#683	1	4	yes	—
341	C₃	#10613955	1	1	yes	characteristic, direct product factor, Sylow
342	C₂	—	2	4	no	—
343	C₂	C₃×#65851	1	2	yes	—
344	C₂	C₃×D₅×#117	1	2	yes	—
345	C₂	C₂²×C₃×#683	1	1	yes	characteristic
346	C₂	C₃×#66166	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₃×#2285
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
4. C₃×#65266	C₂	semidirect
5. C₃×#65265	C₂	semidirect
7. C₃×C₄×#683	C₂	semidirect
8. #10613955	C₃	direct (N × H)
19. C₂×C₃×C₄×Dic₅	C₄	semidirect
29. #65266	C₂×C₃	semidirect
30. #65265	C₂×C₃	semidirect
32. C₄×#683	C₂×C₃	semidirect
72. C₂×C₄×Dic₅	C₃×C₄	semidirect
86. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
158. C₃×Dic₅	#117	semidirect
188. C₂×C₄×C₅	C₃×C₄⋊C₄	semidirect
237. C₂×C₃×C₄	#683	semidirect
257. Dic₅	C₃×#117	semidirect
280. C₃×C₅	#2285	semidirect
314. C₂×C₄	C₃×#683	semidirect
326. C₅	C₃×#2285	semidirect
341. C₃	#10613955	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×#117	2
C₂×C₃×#4072	2
C₂²×C₃×C₄×Dic₅	2
C₃×#65266	2
C₃×#65265	2
C₃×#65231	2
C₃×C₄×#683	2
#10613955	3
C₃×#2285	5

Subgroups — C3×#10613955 #14320148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613955 #14320148