Subgroups — C₃×D₅×#349 #14312895

Order 1920.

472 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅×M₃₂	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64773	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64734	C₂	1	2	yes	maximal, complemented
6	D₅×#349	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₃×#681	C₄	1	1	yes	characteristic
10	C₃×D₅×M₁₆	—	2	2	no	—
11	C₃×D₅×M₁₆	—	2	2	no	—
12	C₂×C₃×#676	C₄	1	1	yes	characteristic
13	C₂×C₃×#676	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic
15	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×M₃₂	C₂²	1	2	yes	complemented
17	C₃×#3944	C₂²	1	2	yes	complemented
18	C₃×#3930	—	2	2	no	—
19	C₃×D₅×C₁₆	—	2	2	no	—
20	C₂×C₃×#349	—	5	1	no	maximal, Hall
21	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
22	D₅×M₃₂	C₂×C₃	1	2	yes	complemented
23	C₅×#349	C₂×C₃	1	1	yes	characteristic, complemented
24	#64773	C₂×C₃	1	1	yes	characteristic, complemented
25	#64734	C₂×C₃	1	2	yes	complemented
26	C₂³×C₃×D₅	C₈	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×Dic₅	C₈	1	1	yes	characteristic
29	C₂×C₃×C₄×D₅	—	2	1	no	—
30	C₂×C₃×C₄×D₅	—	2	1	no	—
31	C₂×C₃×C₄×D₅	—	2	1	no	—
32	C₂×C₃×C₄×D₅	—	2	1	no	—
33	C₂×C₃×C₄×D₅	C₈	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	C₈	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
37	C₃×C₅×M₁₆	—	2	2	no	—
38	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
40	C₃×#681	—	2	2	no	—
41	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
43	C₃×#676	—	2	2	no	—
44	C₃×#676	—	2	2	no	—
45	C₃×C₈×D₅	—	2	1	no	—
46	C₃×C₈×D₅	—	2	1	no	—
47	C₃×C₈×D₅	D₄	1	2	yes	—
48	C₃×C₈×D₅	D₄	1	2	yes	—
49	C₃×C₅×C₁₆	—	2	2	no	—
50	C₃×#672	—	2	2	no	—
51	C₂²×C₃×M₁₆	—	5	1	no	—
52	C₂×C₃×M₃₂	—	5	2	no	—
53	C₃×#349	—	5	1	no	—
54	C₃×#349	—	5	2	no	—
55	C₃×#349	D₅	1	1	yes	characteristic, direct product factor
56	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
57	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
58	C₂×#681	C₃×C₄	1	1	yes	characteristic
59	D₅×M₁₆	—	2	2	no	—
60	D₅×M₁₆	—	2	2	no	—
61	C₂×#676	C₃×C₄	1	1	yes	characteristic
62	C₂×#676	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₈×D₅	C₃×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
65	C₅×M₃₂	C₂²×C₃	1	2	yes	complemented
66	#3944	C₂²×C₃	1	2	yes	complemented
67	#3930	—	2	2	no	—
68	D₅×C₁₆	—	2	2	no	—
69	C₂×#349	—	5	1	no	Sylow
70	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
71	C₂²×C₃×D₅	—	2	1	no	—
72	C₂²×C₃×D₅	—	2	1	no	—
73	C₂²×C₃×D₅	—	4	2	no	—
74	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
75	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	—	2	1	no	—
78	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₃×Dic₅	—	2	1	no	—
81	C₂×C₃×Dic₅	—	2	1	no	—
82	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
83	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
84	C₃×C₄×D₅	—	2	1	no	—
85	C₃×C₄×D₅	—	2	1	no	—
86	C₃×C₄×D₅	—	2	1	no	—
87	C₃×C₄×D₅	—	2	1	no	—
88	C₃×C₄×D₅	—	2	1	no	—
89	C₃×C₄×D₅	—	2	1	no	—
90	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₃×C₄×D₅	M₁₆	1	1	yes	characteristic
93	C₃×C₄×D₅	M₁₆	1	1	yes	characteristic
94	C₃×C₅×C₈	—	2	1	no	—
95	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
96	C₃×#168	—	2	1	no	—
97	C₃×#168	C₂²⋊C₄	1	2	yes	—
98	C₂³×C₃×C₄	—	5	1	no	—
99	C₂×C₃×M₁₆	—	5	1	no	—
100	C₂×C₃×M₁₆	—	5	1	no	—
101	C₂×C₃×M₁₆	—	5	1	no	—
102	C₂×C₃×M₁₆	—	10	2	no	—
103	C₂×C₃×M₁₆	—	10	2	no	—
104	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
105	C₂²×C₃×C₈	—	5	1	no	—
106	C₂²×C₃×C₈	—	5	1	no	—
107	C₃×M₃₂	—	5	2	no	—
108	C₃×M₃₂	—	10	2	no	—
109	C₃×M₃₂	C₂×D₅	1	2	yes	complemented
110	C₂×C₃×C₁₆	—	10	2	no	—
111	C₂³×D₅	C₃×C₈	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂²×Dic₅	C₃×C₈	1	1	yes	characteristic
114	C₂×C₄×D₅	—	2	1	no	—
115	C₂×C₄×D₅	—	2	1	no	—
116	C₂×C₄×D₅	—	2	1	no	—
117	C₂×C₄×D₅	—	2	1	no	—
118	C₂×C₄×D₅	C₃×C₈	1	1	yes	characteristic
119	C₂×C₄×D₅	C₃×C₈	1	1	yes	characteristic
120	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
122	C₅×M₁₆	—	2	2	no	—
123	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
125	#681	—	2	2	no	—
126	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
128	#676	—	2	2	no	—
129	#676	—	2	2	no	—
130	C₈×D₅	—	2	1	no	—
131	C₈×D₅	—	2	1	no	—
132	C₈×D₅	C₃×D₄	1	2	yes	—
133	C₈×D₅	C₃×D₄	1	2	yes	—
134	C₅×C₁₆	—	2	2	no	—
135	#672	—	2	2	no	—
136	C₂²×M₁₆	—	5	1	no	—
137	C₂×M₃₂	—	5	2	no	—
138	#349	—	5	1	no	—
139	#349	—	5	2	no	—
140	#349	C₃×D₅	1	1	yes	characteristic, direct product factor
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	—	4	1	no	—
143	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₃×D₅	—	2	2	no	—
145	C₂×C₃×D₅	—	2	1	no	—
146	C₂×C₃×D₅	—	4	2	no	—
147	C₂×C₃×D₅	—	4	2	no	—
148	C₂×C₃×D₅	—	4	1	no	—
149	C₂×C₃×D₅	C₂²⋊C₈	1	1	yes	characteristic
150	C₂×C₃×D₅	C₂²⋊C₈	1	1	yes	characteristic
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
154	C₃×Dic₅	—	2	1	no	—
155	C₃×Dic₅	C₂²⋊C₈	1	1	yes	characteristic
156	C₃×Dic₅	C₂²⋊C₈	1	1	yes	characteristic
157	C₂⁴×C₃	—	5	1	no	—
158	C₂²×C₃×C₄	—	5	1	no	—
159	C₂²×C₃×C₄	—	5	1	no	—
160	C₂²×C₃×C₄	—	5	1	no	—
161	C₂²×C₃×C₄	—	5	1	no	—
162	C₂²×C₃×C₄	—	5	1	no	—
163	C₂²×C₃×C₄	—	10	1	no	—
164	C₂²×C₃×C₄	—	10	1	no	—
165	C₂²×C₃×C₄	—	10	1	no	—
166	C₂²×C₃×C₄	—	10	1	no	—
167	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
168	C₃×M₁₆	—	2	2	no	—
169	C₃×M₁₆	—	10	2	no	—
170	C₃×M₁₆	—	10	2	no	—
171	C₃×M₁₆	—	10	2	no	—
172	C₂×C₃×C₈	—	5	1	no	—
173	C₂×C₃×C₈	—	5	2	no	—
174	C₂×C₃×C₈	—	5	2	no	—
175	C₂×C₃×C₈	—	5	1	no	—
176	C₂×C₃×C₈	—	10	1	no	—
177	C₂×C₃×C₈	—	10	1	no	—
178	C₂×C₃×C₈	C₄×D₅	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
180	C₃×C₁₆	—	2	2	no	—
181	C₃×C₁₆	—	10	2	no	—
182	C₂³×C₅	C₂×C₃×C₈	1	1	yes	characteristic
183	C₂²×D₅	—	2	1	no	—
184	C₂²×D₅	—	2	1	no	—
185	C₂²×D₅	—	4	2	no	—
186	C₂²×D₅	C₂×C₃×C₈	1	1	yes	characteristic
187	C₂²×D₅	C₂×C₃×C₈	1	1	yes	characteristic
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
192	C₂×Dic₅	—	2	1	no	—
193	C₂×Dic₅	—	2	1	no	—
194	C₂×Dic₅	C₂×C₃×C₈	1	1	yes	characteristic
195	C₂×Dic₅	C₂×C₃×C₈	1	1	yes	characteristic
196	C₄×D₅	—	2	1	no	—
197	C₄×D₅	—	2	1	no	—
198	C₄×D₅	—	2	1	no	—
199	C₄×D₅	—	2	1	no	—
200	C₄×D₅	—	2	1	no	—
201	C₄×D₅	—	2	1	no	—
202	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₄×D₅	C₃×M₁₆	1	1	yes	characteristic
205	C₄×D₅	C₃×M₁₆	1	1	yes	characteristic
206	C₅×C₈	—	2	1	no	—
207	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
208	#168	—	2	1	no	—
209	#168	C₃×C₂²⋊C₄	1	2	yes	—
210	C₂³×C₄	—	5	1	no	—
211	C₂×M₁₆	—	5	1	no	—
212	C₂×M₁₆	—	5	1	no	—
213	C₂×M₁₆	—	5	1	no	—
214	C₂×M₁₆	—	10	2	no	—
215	C₂×M₁₆	—	10	2	no	—
216	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
217	C₂²×C₈	—	5	1	no	—
218	C₂²×C₈	—	5	1	no	—
219	M₃₂	—	5	2	no	—
220	M₃₂	—	10	2	no	—
221	M₃₂	C₂×C₃×D₅	1	2	yes	complemented
222	C₂×C₁₆	—	10	2	no	—
223	C₂×C₃×C₅	—	2	1	no	—
224	C₂×C₃×C₅	—	4	1	no	—
225	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
226	C₃×D₅	—	2	1	no	—
227	C₃×D₅	—	4	1	no	—
228	C₃×D₅	#349	1	2	yes	direct product factor
229	C₂³×C₃	—	5	1	no	—
230	C₂³×C₃	—	5	1	no	—
231	C₂³×C₃	—	10	1	no	—
232	C₂³×C₃	—	10	1	no	—
233	C₂³×C₃	—	20	2	no	—
234	C₂³×C₃	C₈×D₅	1	1	yes	characteristic
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	5	1	no	—
238	C₂×C₃×C₄	—	5	1	no	—
239	C₂×C₃×C₄	—	5	1	no	—
240	C₂×C₃×C₄	—	5	1	no	—
241	C₂×C₃×C₄	—	5	1	no	—
242	C₂×C₃×C₄	—	5	1	no	—
243	C₂×C₃×C₄	—	10	1	no	—
244	C₂×C₃×C₄	—	10	1	no	—
245	C₂×C₃×C₄	—	10	1	no	—
246	C₂×C₃×C₄	—	10	1	no	—
247	C₂×C₃×C₄	—	10	1	no	—
248	C₂×C₃×C₄	—	10	1	no	—
249	C₂×C₃×C₄	—	10	1	no	—
250	C₂×C₃×C₄	—	10	1	no	—
251	C₂×C₃×C₄	C₈×D₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
253	C₃×C₈	—	2	1	no	—
254	C₃×C₈	—	5	2	no	—
255	C₃×C₈	—	10	1	no	—
256	C₃×C₈	D₄×D₅	1	2	yes	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	4	1	no	—
259	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
260	C₂×D₅	—	2	2	no	—
261	C₂×D₅	—	2	1	no	—
262	C₂×D₅	—	4	2	no	—
263	C₂×D₅	—	4	2	no	—
264	C₂×D₅	—	4	1	no	—
265	C₂×D₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
266	C₂×D₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
270	Dic₅	—	2	1	no	—
271	Dic₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
272	Dic₅	C₃×C₂²⋊C₈	1	1	yes	characteristic
273	C₂⁴	—	5	1	no	—
274	C₂²×C₄	—	5	1	no	—
275	C₂²×C₄	—	5	1	no	—
276	C₂²×C₄	—	5	1	no	—
277	C₂²×C₄	—	5	1	no	—
278	C₂²×C₄	—	5	1	no	—
279	C₂²×C₄	—	10	1	no	—
280	C₂²×C₄	—	10	1	no	—
281	C₂²×C₄	—	10	1	no	—
282	C₂²×C₄	—	10	1	no	—
283	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
284	M₁₆	—	2	2	no	—
285	M₁₆	—	10	2	no	—
286	M₁₆	—	10	2	no	—
287	M₁₆	—	10	2	no	—
288	C₂×C₈	—	5	1	no	—
289	C₂×C₈	—	5	2	no	—
290	C₂×C₈	—	5	2	no	—
291	C₂×C₈	—	5	1	no	—
292	C₂×C₈	—	10	1	no	—
293	C₂×C₈	—	10	1	no	—
294	C₂×C₈	C₃×C₄×D₅	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
296	C₁₆	—	2	2	no	—
297	C₁₆	—	10	2	no	—
298	C₃×C₅	C₂×#349	1	1	yes	characteristic, complemented, Hall
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	5	1	no	—
302	C₂²×C₃	—	5	1	no	—
303	C₂²×C₃	—	10	2	no	—
304	C₂²×C₃	—	10	1	no	—
305	C₂²×C₃	—	20	1	no	—
306	C₂²×C₃	—	20	2	no	—
307	C₂²×C₃	—	20	2	no	—
308	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	5	1	no	—
311	C₃×C₄	—	5	1	no	—
312	C₃×C₄	—	10	1	no	—
313	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
314	C₃×C₄	D₅×M₁₆	1	1	yes	characteristic
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	4	1	no	—
317	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
318	D₅	—	2	1	no	—
319	D₅	—	4	1	no	—
320	D₅	C₃×#349	1	2	yes	direct product factor
321	C₂³	—	5	1	no	—
322	C₂³	—	5	1	no	—
323	C₂³	—	10	1	no	—
324	C₂³	—	10	1	no	—
325	C₂³	—	20	2	no	—
326	C₂³	C₃×C₈×D₅	1	1	yes	characteristic
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	5	1	no	—
330	C₂×C₄	—	5	1	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	1	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	5	1	no	—
335	C₂×C₄	—	10	1	no	—
336	C₂×C₄	—	10	1	no	—
337	C₂×C₄	—	10	1	no	—
338	C₂×C₄	—	10	1	no	—
339	C₂×C₄	—	10	1	no	—
340	C₂×C₄	—	10	1	no	—
341	C₂×C₄	—	10	1	no	—
342	C₂×C₄	—	10	1	no	—
343	C₂×C₄	C₃×C₈×D₅	1	1	yes	characteristic
344	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	5	2	no	—
347	C₈	—	10	1	no	—
348	C₈	C₃×D₄×D₅	1	2	yes	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	4	1	no	—
351	C₂×C₃	—	5	2	no	—
352	C₂×C₃	—	10	1	no	—
353	C₂×C₃	—	20	1	no	—
354	C₂×C₃	D₅×C₂²⋊C₈	1	1	yes	characteristic
355	C₅	C₂×C₃×#349	1	1	yes	characteristic, complemented, Sylow
356	C₂²	—	2	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	5	1	no	—
359	C₂²	—	5	1	no	—
360	C₂²	—	10	2	no	—
361	C₂²	—	10	1	no	—
362	C₂²	—	20	1	no	—
363	C₂²	—	20	2	no	—
364	C₂²	—	20	2	no	—
365	C₂²	C₂×C₃×C₈×D₅	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	5	1	no	—
368	C₄	—	5	1	no	—
369	C₄	—	10	1	no	—
370	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
371	C₄	C₃×D₅×M₁₆	1	1	yes	characteristic
372	C₃	D₅×#349	1	1	yes	characteristic, direct product factor, Sylow
373	C₂	—	2	1	no	—
374	C₂	—	4	1	no	—
375	C₂	—	5	2	no	—
376	C₂	—	10	1	no	—
377	C₂	—	20	1	no	—
378	C₂	C₃×D₅×C₂²⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₅×C₂²⋊C₄
commutator	C₂²×C₅	C₂²×C₃×C₈
Frattini	C₂×C₈	C₂²×C₃×D₅
Fitting	C₃×C₅×#349	C₂
socle	C₂×C₃×C₅	C₂×C₂²⋊C₈
prime radical	C₂³×C₃×D₅	C₈
cosocle	C₂×C₅×C₈	C₂³×C₃
hypercenter	C₃×#349	D₅
hypocenter	C₅	C₂×C₃×#349
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#349

Complements

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

N	H ≅ G/N	type
2. C₃×D₅×M₃₂	C₂	semidirect
3. C₃×C₅×#349	C₂	semidirect
4. C₃×#64773	C₂	semidirect
5. C₃×#64734	C₂	semidirect
6. D₅×#349	C₃	direct (N × H)
16. C₃×C₅×M₃₂	C₂²	semidirect
17. C₃×#3944	C₂²	semidirect
22. D₅×M₃₂	C₂×C₃	semidirect
23. C₅×#349	C₂×C₃	semidirect
24. #64773	C₂×C₃	semidirect
25. #64734	C₂×C₃	semidirect
55. C₃×#349	D₅	direct (N × H)
65. C₅×M₃₂	C₂²×C₃	semidirect
66. #3944	C₂²×C₃	semidirect
109. C₃×M₃₂	C₂×D₅	semidirect
140. #349	C₃×D₅	direct (N × H)
221. M₃₂	C₂×C₃×D₅	semidirect
228. C₃×D₅	#349	direct (N × H)
298. C₃×C₅	C₂×#349	semidirect
320. D₅	C₃×#349	direct (N × H)
355. C₅	C₂×C₃×#349	semidirect
372. C₃	D₅×#349	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×D₅×M₁₆	2
C₃×D₅×M₃₂	2
C₃×C₅×#349	2
C₃×#64773	2
C₃×#64734	2
D₅×#349	3
C₂×C₃×#349	5

Subgroups — C3×D5×#349 #14312895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#349 #14312895