Subgroups — C₃×#65990 #11755667

Order 960.

660 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×#711	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4042	C₂	1	2	yes	maximal, complemented
7	C₃×#4039	C₂	1	2	yes	maximal, complemented
8	C₃×#4030	C₂	1	2	yes	maximal, complemented
9	C₃×#4028	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4027	C₂	1	2	yes	maximal, complemented
11	C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
12	#65990	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
21	C₃×#711	—	2	4	no	—
22	C₂×C₃×D₂₀	C₂²	1	2	yes	—
23	C₂×C₃×C₄×D₅	—	2	4	no	—
24	C₂×C₃×C₄×D₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄×D₅	C₂²	1	2	yes	—
26	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
31	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
32	C₃×#685	C₂²	1	2	yes	—
33	C₃×#685	C₂²	1	2	yes	—
34	C₃×#685	C₂²	1	2	yes	complemented
35	C₃×#683	C₂²	1	2	yes	complemented
36	C₃×#683	C₂²	1	2	yes	complemented
37	C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
38	C₃×#525	—	5	1	no	maximal, Hall
39	C₂×#711	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂²×C₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
42	#4083	C₂×C₃	1	1	yes	characteristic, complemented
43	#4075	C₂×C₃	1	1	yes	characteristic, complemented
44	#4042	C₂×C₃	1	2	yes	complemented
45	#4039	C₂×C₃	1	2	yes	complemented
46	#4030	C₂×C₃	1	2	yes	complemented
47	#4028	C₂×C₃	1	1	yes	characteristic, complemented
48	#4027	C₂×C₃	1	2	yes	complemented
49	#4023	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×D₅	—	2	2	no	—
53	C₂²×C₃×D₅	—	2	4	no	—
54	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×D₅	C₂³	1	2	yes	—
56	C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₄×C₅	—	2	2	no	—
58	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₂²⋊D₅	—	2	2	no	—
62	C₃×C₂²⋊D₅	—	2	4	no	—
63	C₃×C₂²⋊D₅	—	2	2	no	—
64	C₂×C₃×Dic₅	—	2	2	no	—
65	C₂×C₃×Dic₅	D₄	1	4	yes	complemented
66	C₂×C₃×Dic₅	C₂³	1	2	yes	—
67	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
70	C₃×D₂₀	—	2	4	no	—
71	C₃×C₄×D₅	—	2	4	no	—
72	C₃×C₄×D₅	—	2	4	no	—
73	C₃×C₄×D₅	—	2	2	no	—
74	C₃×Dic₁₀	—	2	2	no	—
75	C₂×C₃×#41	—	5	1	no	—
76	C₂³×C₃×C₄	—	5	1	no	—
77	C₃×#123	—	5	1	no	—
78	C₃×#123	D₅	1	1	yes	characteristic, complemented
79	C₃×C₂²⋊Q₈	—	5	2	no	—
80	C₃×#121	—	5	2	no	—
81	C₃×#120	—	5	1	no	—
82	C₃×#120	—	5	1	no	—
83	C₃×C₄×D₄	—	5	2	no	—
84	C₃×C₄×D₄	—	5	2	no	—
85	C₃×#117	—	5	1	no	—
86	C₂³×D₅	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
91	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
93	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
94	#711	—	2	4	no	—
95	C₂×D₂₀	C₂²×C₃	1	2	yes	—
96	C₂×C₄×D₅	—	2	4	no	—
97	C₂×C₄×D₅	C₂²×C₃	1	2	yes	—
98	C₂×C₄×D₅	C₂²×C₃	1	2	yes	—
99	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
102	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
104	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
105	#685	C₂²×C₃	1	2	yes	—
106	#685	C₂²×C₃	1	2	yes	—
107	#685	C₂²×C₃	1	2	yes	complemented
108	#683	C₂²×C₃	1	2	yes	complemented
109	#683	C₂²×C₃	1	2	yes	complemented
110	C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
111	#525	—	5	1	no	Sylow
112	C₂²×C₃×C₅	—	2	2	no	—
113	C₂²×C₃×C₅	—	2	1	no	—
114	C₂²×C₃×C₅	—	2	2	no	—
115	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
116	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
117	C₂×C₃×D₅	—	2	8	no	—
118	C₂×C₃×D₅	—	2	2	no	—
119	C₂×C₃×D₅	—	2	2	no	—
120	C₂×C₃×D₅	—	2	1	no	—
121	C₂×C₃×D₅	—	2	2	no	—
122	C₂×C₃×D₅	#41	1	4	yes	complemented
123	C₃×C₄×C₅	—	2	1	no	—
124	C₃×C₄×C₅	—	2	2	no	—
125	C₃×C₄×C₅	—	2	2	no	—
126	C₃×Dic₅	—	2	1	no	—
127	C₃×Dic₅	—	2	2	no	—
128	C₃×Dic₅	C₂×D₄	1	2	yes	—
129	C₃×Dic₅	C₂×D₄	1	2	yes	—
130	C₂⁴×C₃	—	5	1	no	—
131	C₃×#41	—	10	4	no	—
132	C₂×C₃×Q₈	—	5	1	no	—
133	C₂×C₃×D₄	—	5	2	no	—
134	C₂×C₃×D₄	—	5	1	no	—
135	C₂×C₃×D₄	—	5	1	no	—
136	C₂×C₃×D₄	—	5	2	no	—
137	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic
138	C₂²×C₃×C₄	—	5	1	no	—
139	C₂²×C₃×C₄	—	5	1	no	—
140	C₂²×C₃×C₄	—	5	2	no	—
141	C₂²×C₃×C₄	—	5	2	no	—
142	C₂²×C₃×C₄	—	5	1	no	—
143	C₂²×C₃×C₄	—	10	4	no	—
144	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
145	C₃×C₄⋊C₄	—	5	2	no	—
146	C₃×C₄⋊C₄	—	5	2	no	—
147	C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
148	C₃×C₂²⋊C₄	—	5	1	no	—
149	C₃×C₂²⋊C₄	—	5	2	no	—
150	C₃×C₂²⋊C₄	—	5	2	no	—
151	C₃×C₂²⋊C₄	—	5	2	no	—
152	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
153	C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
154	C₃×C₄²	—	5	2	no	—
155	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₂²×D₅	—	2	2	no	—
158	C₂²×D₅	—	2	4	no	—
159	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×D₅	C₂³×C₃	1	2	yes	—
161	C₅×D₄	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
165	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₂²⋊D₅	—	2	2	no	—
167	C₂²⋊D₅	—	2	4	no	—
168	C₂²⋊D₅	—	2	2	no	—
169	C₂×Dic₅	—	2	2	no	—
170	C₂×Dic₅	C₃×D₄	1	4	yes	complemented
171	C₂×Dic₅	C₂³×C₃	1	2	yes	—
172	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
173	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
174	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
175	D₂₀	—	2	4	no	—
176	C₄×D₅	—	2	4	no	—
177	C₄×D₅	—	2	4	no	—
178	C₄×D₅	—	2	2	no	—
179	Dic₁₀	—	2	2	no	—
180	C₂×#41	—	5	1	no	—
181	C₂³×C₄	—	5	1	no	—
182	#123	—	5	1	no	—
183	#123	C₃×D₅	1	1	yes	characteristic, complemented
184	C₂²⋊Q₈	—	5	2	no	—
185	#121	—	5	2	no	—
186	#120	—	5	1	no	—
187	#120	—	5	1	no	—
188	C₄×D₄	—	5	2	no	—
189	C₄×D₄	—	5	2	no	—
190	#117	—	5	1	no	—
191	C₂×C₃×C₅	—	2	2	no	—
192	C₂×C₃×C₅	—	4	1	no	—
193	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₃×C₅	C₂×#41	1	2	yes	—
195	C₃×D₅	—	2	4	no	—
196	C₃×D₅	—	4	1	no	—
197	C₂³×C₃	—	5	2	no	—
198	C₂³×C₃	—	5	1	no	—
199	C₂³×C₃	—	10	4	no	—
200	C₂³×C₃	—	10	2	no	—
201	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
202	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
203	C₃×Q₈	—	10	2	no	—
204	C₃×D₄	—	2	2	no	—
205	C₃×D₄	—	10	4	no	—
206	C₃×D₄	—	10	2	no	—
207	C₃×D₄	—	10	4	no	—
208	C₃×D₄	—	10	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	5	4	no	—
211	C₂×C₃×C₄	—	5	1	no	—
212	C₂×C₃×C₄	—	5	1	no	—
213	C₂×C₃×C₄	—	5	2	no	—
214	C₂×C₃×C₄	—	5	1	no	—
215	C₂×C₃×C₄	—	10	4	no	—
216	C₂×C₃×C₄	—	10	4	no	—
217	C₂×C₃×C₄	—	10	2	no	—
218	C₂×C₃×C₄	—	10	2	no	—
219	C₂×C₃×C₄	C₂²×D₅	1	2	yes	—
220	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
221	C₂×C₃×C₄	C₂²×D₅	1	2	yes	—
222	C₂²×C₅	—	2	2	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	C₂×C₃×D₄	1	2	yes	—
226	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₂×D₅	—	2	8	no	—
228	C₂×D₅	—	2	2	no	—
229	C₂×D₅	—	2	2	no	—
230	C₂×D₅	—	2	1	no	—
231	C₂×D₅	—	2	2	no	—
232	C₂×D₅	C₃×#41	1	4	yes	complemented
233	C₄×C₅	—	2	1	no	—
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	2	2	no	—
236	Dic₅	—	2	1	no	—
237	Dic₅	—	2	2	no	—
238	Dic₅	C₂×C₃×D₄	1	2	yes	—
239	Dic₅	C₂×C₃×D₄	1	2	yes	—
240	C₂⁴	—	5	1	no	—
241	#41	—	10	4	no	—
242	C₂×Q₈	—	5	1	no	—
243	C₂×D₄	—	5	2	no	—
244	C₂×D₄	—	5	1	no	—
245	C₂×D₄	—	5	1	no	—
246	C₂×D₄	—	5	2	no	—
247	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic
248	C₂²×C₄	—	5	1	no	—
249	C₂²×C₄	—	5	1	no	—
250	C₂²×C₄	—	5	2	no	—
251	C₂²×C₄	—	5	1	no	—
252	C₂²×C₄	—	5	2	no	—
253	C₂²×C₄	—	10	4	no	—
254	C₂²×C₄	C₂×C₃×D₅	1	1	yes	characteristic
255	C₄⋊C₄	—	5	2	no	—
256	C₄⋊C₄	—	5	2	no	—
257	C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
258	C₂²⋊C₄	—	5	1	no	—
259	C₂²⋊C₄	—	5	2	no	—
260	C₂²⋊C₄	—	5	2	no	—
261	C₂²⋊C₄	—	5	2	no	—
262	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
263	C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
264	C₄²	—	5	2	no	—
265	C₃×C₅	#525	1	1	yes	characteristic, complemented, Hall
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	5	4	no	—
270	C₂²×C₃	—	10	8	no	—
271	C₂²×C₃	—	10	2	no	—
272	C₂²×C₃	—	10	2	no	—
273	C₂²×C₃	—	10	1	no	—
274	C₂²×C₃	—	10	2	no	—
275	C₂²×C₃	D₄×D₅	1	2	yes	—
276	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
277	C₃×C₄	—	2	2	no	—
278	C₃×C₄	—	2	1	no	—
279	C₃×C₄	—	2	2	no	—
280	C₃×C₄	—	5	2	no	—
281	C₃×C₄	—	5	2	no	—
282	C₃×C₄	—	10	1	no	—
283	C₃×C₄	—	10	2	no	—
284	C₂×C₅	—	2	2	no	—
285	C₂×C₅	—	4	1	no	—
286	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
287	C₂×C₅	C₂×C₃×#41	1	2	yes	—
288	D₅	—	2	4	no	—
289	D₅	—	4	1	no	—
290	C₂³	—	5	2	no	—
291	C₂³	—	5	1	no	—
292	C₂³	—	10	4	no	—
293	C₂³	—	10	2	no	—
294	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
295	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
296	Q₈	—	10	2	no	—
297	D₄	—	2	2	no	—
298	D₄	—	10	4	no	—
299	D₄	—	10	2	no	—
300	D₄	—	10	4	no	—
301	D₄	—	10	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	5	4	no	—
304	C₂×C₄	—	5	1	no	—
305	C₂×C₄	—	5	1	no	—
306	C₂×C₄	—	5	2	no	—
307	C₂×C₄	—	5	1	no	—
308	C₂×C₄	—	10	4	no	—
309	C₂×C₄	—	10	4	no	—
310	C₂×C₄	—	10	2	no	—
311	C₂×C₄	—	10	2	no	—
312	C₂×C₄	C₂²×C₃×D₅	1	2	yes	—
313	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₃×D₅	1	2	yes	—
315	C₂×C₃	—	2	2	no	—
316	C₂×C₃	—	4	1	no	—
317	C₂×C₃	—	10	4	no	—
318	C₂×C₃	—	20	1	no	—
319	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
320	C₂×C₃	D₅×#41	1	2	yes	—
321	C₅	C₃×#525	1	1	yes	characteristic, complemented, Sylow
322	C₂²	—	2	2	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	5	4	no	—
326	C₂²	—	10	8	no	—
327	C₂²	—	10	2	no	—
328	C₂²	—	10	2	no	—
329	C₂²	—	10	1	no	—
330	C₂²	—	10	2	no	—
331	C₂²	C₃×D₄×D₅	1	2	yes	—
332	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
333	C₄	—	2	2	no	—
334	C₄	—	2	1	no	—
335	C₄	—	2	2	no	—
336	C₄	—	5	2	no	—
337	C₄	—	5	2	no	—
338	C₄	—	10	1	no	—
339	C₄	—	10	2	no	—
340	C₃	#65990	1	1	yes	characteristic, direct product factor, Sylow
341	C₂	—	2	2	no	—
342	C₂	—	4	1	no	—
343	C₂	—	10	4	no	—
344	C₂	—	20	1	no	—
345	C₂	C₂×C₃×D₄×D₅	1	1	yes	characteristic
346	C₂	C₃×D₅×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₅×#123	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₃×#123	D₅
hypocenter	C₅	C₃×#525
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#711	C₂	semidirect
2. C₂²×C₃×C₄×D₅	C₂	semidirect
3. C₃×C₅×#123	C₂	semidirect
4. C₃×#4083	C₂	semidirect
5. C₃×#4075	C₂	semidirect
6. C₃×#4042	C₂	semidirect
7. C₃×#4039	C₂	semidirect
8. C₃×#4030	C₂	semidirect
9. C₃×#4028	C₂	semidirect
10. C₃×#4027	C₂	semidirect
11. C₃×#4023	C₂	semidirect
12. #65990	C₃	direct (N × H)
18. C₂×C₃×C₂²⋊D₅	C₂²	semidirect
20. C₂²×C₃×Dic₅	C₂²	semidirect
26. C₂×C₃×C₄×D₅	C₂²	semidirect
27. C₂×C₃×Dic₁₀	C₂²	semidirect
28. C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. C₃×#685	C₂²	semidirect
35. C₃×#683	C₂²	semidirect
36. C₃×#683	C₂²	semidirect
37. C₃×C₄×Dic₅	C₂²	semidirect
39. C₂×#711	C₂×C₃	semidirect
40. C₂²×C₄×D₅	C₂×C₃	semidirect
41. C₅×#123	C₂×C₃	semidirect
42. #4083	C₂×C₃	semidirect
43. #4075	C₂×C₃	semidirect
44. #4042	C₂×C₃	semidirect
45. #4039	C₂×C₃	semidirect
46. #4030	C₂×C₃	semidirect
47. #4028	C₂×C₃	semidirect
48. #4027	C₂×C₃	semidirect
49. #4023	C₂×C₃	semidirect
65. C₂×C₃×Dic₅	D₄	semidirect
78. C₃×#123	D₅	semidirect
91. C₂×C₂²⋊D₅	C₂²×C₃	semidirect
93. C₂²×Dic₅	C₂²×C₃	semidirect
99. C₂×C₄×D₅	C₂²×C₃	semidirect
100. C₂×Dic₁₀	C₂²×C₃	semidirect
101. C₅×C₄⋊C₄	C₂²×C₃	semidirect
103. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
107. #685	C₂²×C₃	semidirect
108. #683	C₂²×C₃	semidirect
109. #683	C₂²×C₃	semidirect
110. C₄×Dic₅	C₂²×C₃	semidirect
122. C₂×C₃×D₅	#41	semidirect
147. C₃×C₄⋊C₄	C₂×D₅	semidirect
153. C₃×C₂²⋊C₄	C₂×D₅	semidirect
170. C₂×Dic₅	C₃×D₄	semidirect
183. #123	C₃×D₅	semidirect
232. C₂×D₅	C₃×#41	semidirect
257. C₄⋊C₄	C₂×C₃×D₅	semidirect
263. C₂²⋊C₄	C₂×C₃×D₅	semidirect
265. C₃×C₅	#525	semidirect
321. C₅	C₃×#525	semidirect
340. C₃	#65990	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×#711	2
C₂²×C₃×C₄×D₅	2
C₃×C₅×#123	2
C₃×#4083	2
C₃×#4075	2
C₃×#4042	2
C₃×#4039	2
C₃×#4030	2
C₃×#4028	2
C₃×#4027	2
C₃×#4023	2
#65990	3
C₃×#525	5

Subgroups — C3×#65990 #11755667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65990 #11755667