Subgroups — C₃×#65879 #11755556

Order 960.

676 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#685	C₂	1	2	yes	maximal, complemented
6	C₃×#4039	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4027	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
12	#65879	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₅	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₅	C₂²	1	2	yes	complemented
16	C₂×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂²×C₃×Dic₅	C₂²	1	2	yes	complemented
18	C₃×D₄×D₅	C₄	1	8	yes	complemented
19	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄×D₅	C₂²	1	2	yes	complemented
22	C₂×C₃×C₄×D₅	C₂²	1	2	yes	complemented
23	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
27	C₃×#685	C₂²	1	1	yes	characteristic
28	C₃×#685	C₂²	1	1	yes	characteristic
29	C₃×#685	C₂²	1	2	yes	—
30	C₃×#685	C₂²	1	2	yes	complemented
31	C₃×#685	C₂²	1	2	yes	complemented
32	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
33	C₃×#683	C₂²	1	1	yes	characteristic, complemented
34	C₃×#683	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
37	C₃×#518	—	5	1	no	maximal, Hall
38	C₂×D₄×D₅	C₂×C₃	1	1	yes	characteristic
39	C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
40	D₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
42	C₂×#685	C₂×C₃	1	2	yes	complemented
43	#4039	C₂×C₃	1	1	yes	characteristic, complemented
44	#4038	C₂×C₃	1	1	yes	characteristic, complemented
45	#4027	C₂×C₃	1	2	yes	complemented
46	D₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
47	C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
48	#4018	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂³×C₃×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×D₅	—	4	2	no	—
51	C₂²×C₃×D₅	—	4	2	no	—
52	C₂²×C₃×D₅	C₂×C₄	1	8	yes	complemented
53	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×D₅	C₂³	1	2	yes	—
55	C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
56	C₂×C₃×C₄×C₅	—	4	2	no	—
57	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₂²⋊D₅	C₂×C₄	1	8	yes	complemented
62	C₂×C₃×Dic₅	—	4	2	no	—
63	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×Dic₅	C₂³	1	2	yes	—
66	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
67	C₃×D₂₀	C₂×C₄	1	4	yes	complemented
68	C₃×C₄×D₅	—	4	2	no	—
69	C₃×C₄×D₅	—	4	2	no	—
70	C₃×C₄×D₅	C₂×C₄	1	4	yes	complemented
71	C₂²×C₃×D₄	—	5	1	no	—
72	C₃×C₄×D₄	—	5	1	no	—
73	C₃×C₄×D₄	—	5	2	no	—
74	C₃×C₄×D₄	—	5	1	no	—
75	C₃×C₄×D₄	—	5	2	no	—
76	C₃×C₄×D₄	—	5	1	no	—
77	C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
78	C₃×#117	—	5	1	no	—
79	C₃×#117	—	5	1	no	—
80	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
81	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
82	C₂³×D₅	C₂²×C₃	1	2	yes	—
83	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²×C₃	1	2	yes	complemented
85	C₂×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
86	C₂²×Dic₅	C₂²×C₃	1	2	yes	complemented
87	D₄×D₅	C₃×C₄	1	8	yes	complemented
88	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₄×D₅	C₂²×C₃	1	2	yes	complemented
91	C₂×C₄×D₅	C₂²×C₃	1	2	yes	complemented
92	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
94	C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
96	#685	C₂²×C₃	1	1	yes	characteristic
97	#685	C₂²×C₃	1	1	yes	characteristic
98	#685	C₂²×C₃	1	2	yes	—
99	#685	C₂²×C₃	1	2	yes	complemented
100	#685	C₂²×C₃	1	2	yes	complemented
101	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
102	#683	C₂²×C₃	1	1	yes	characteristic, complemented
103	#683	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
106	#518	—	5	1	no	Sylow
107	C₂²×C₃×C₅	—	2	2	no	—
108	C₂²×C₃×C₅	—	2	2	no	—
109	C₂²×C₃×C₅	C₂²×C₄	1	4	yes	—
110	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
111	C₂×C₃×D₅	—	2	2	no	—
112	C₂×C₃×D₅	—	2	2	no	—
113	C₂×C₃×D₅	—	2	1	no	—
114	C₂×C₃×D₅	—	2	1	no	—
115	C₂×C₃×D₅	—	4	8	no	—
116	C₂×C₃×D₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×D₅	C₂²×C₄	1	4	yes	—
118	C₃×C₄×C₅	—	2	1	no	—
119	C₃×C₄×C₅	—	2	2	no	—
120	C₃×C₄×C₅	—	2	1	no	—
121	C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₃×Dic₅	—	2	1	no	—
123	C₃×Dic₅	—	2	2	no	—
124	C₃×Dic₅	—	2	1	no	—
125	C₃×Dic₅	C₂²×C₄	1	2	yes	—
126	C₂⁴×C₃	—	5	2	no	—
127	C₂×C₃×D₄	—	5	2	no	—
128	C₂×C₃×D₄	—	5	8	no	—
129	C₂×C₃×D₄	—	5	1	no	—
130	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic
131	C₂²×C₃×C₄	—	5	1	no	—
132	C₂²×C₃×C₄	—	5	2	no	—
133	C₂²×C₃×C₄	—	5	2	no	—
134	C₂²×C₃×C₄	—	5	2	no	—
135	C₂²×C₃×C₄	C₂×D₅	1	2	yes	complemented
136	C₃×C₄⋊C₄	—	5	1	no	—
137	C₃×C₄⋊C₄	—	5	1	no	—
138	C₃×C₄⋊C₄	—	5	1	no	—
139	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
140	C₃×C₂²⋊C₄	—	5	2	no	—
141	C₃×C₂²⋊C₄	—	5	2	no	—
142	C₃×C₂²⋊C₄	—	5	1	no	—
143	C₃×C₂²⋊C₄	—	5	1	no	—
144	C₃×C₂²⋊C₄	—	5	2	no	—
145	C₃×C₂²⋊C₄	—	5	2	no	—
146	C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
147	C₃×C₄²	—	5	2	no	—
148	C₃×C₄²	—	5	1	no	—
149	C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
150	C₂³×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×D₅	—	4	2	no	—
152	C₂²×D₅	—	4	2	no	—
153	C₂²×D₅	C₂×C₃×C₄	1	8	yes	complemented
154	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
155	C₂²×D₅	C₂³×C₃	1	2	yes	—
156	C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
157	C₂×C₄×C₅	—	4	2	no	—
158	C₂×C₄×C₅	C₂³×C₃	1	2	yes	—
159	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₂²⋊D₅	C₂×C₃×C₄	1	8	yes	complemented
163	C₂×Dic₅	—	4	2	no	—
164	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
165	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
166	C₂×Dic₅	C₂³×C₃	1	2	yes	—
167	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
168	D₂₀	C₂×C₃×C₄	1	4	yes	complemented
169	C₄×D₅	—	4	2	no	—
170	C₄×D₅	—	4	2	no	—
171	C₄×D₅	C₂×C₃×C₄	1	4	yes	complemented
172	C₂²×D₄	—	5	1	no	—
173	C₄×D₄	—	5	1	no	—
174	C₄×D₄	—	5	2	no	—
175	C₄×D₄	—	5	1	no	—
176	C₄×D₄	—	5	2	no	—
177	C₄×D₄	—	5	1	no	—
178	C₄×D₄	C₃×D₅	1	1	yes	characteristic, complemented
179	#117	—	5	1	no	—
180	#117	—	5	1	no	—
181	C₂×C₂²⋊C₄	—	5	2	no	—
182	C₂×C₂²⋊C₄	—	5	2	no	—
183	C₂×C₃×C₅	—	2	4	no	—
184	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
187	C₃×D₅	—	2	2	no	—
188	C₃×D₅	—	2	4	no	—
189	C₂³×C₃	—	5	1	no	—
190	C₂³×C₃	—	5	2	no	—
191	C₂³×C₃	—	5	8	no	—
192	C₂³×C₃	—	20	2	no	—
193	C₂³×C₃	—	20	2	no	—
194	C₂³×C₃	C₂²×D₅	1	2	yes	—
195	C₃×D₄	—	5	8	no	—
196	C₃×D₄	—	5	4	no	—
197	C₃×D₄	C₄×D₅	1	4	yes	complemented
198	C₂×C₃×C₄	—	4	2	no	—
199	C₂×C₃×C₄	—	5	1	no	—
200	C₂×C₃×C₄	—	5	4	no	—
201	C₂×C₃×C₄	—	5	1	no	—
202	C₂×C₃×C₄	—	5	1	no	—
203	C₂×C₃×C₄	—	5	2	no	—
204	C₂×C₃×C₄	—	20	2	no	—
205	C₂×C₃×C₄	—	20	2	no	—
206	C₂×C₃×C₄	—	20	2	no	—
207	C₂×C₃×C₄	C₂²×D₅	1	2	yes	—
208	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
210	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
211	C₂²×C₅	—	2	2	no	—
212	C₂²×C₅	—	2	2	no	—
213	C₂²×C₅	C₂²×C₃×C₄	1	4	yes	—
214	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
215	C₂×D₅	—	2	2	no	—
216	C₂×D₅	—	2	2	no	—
217	C₂×D₅	—	2	1	no	—
218	C₂×D₅	—	2	1	no	—
219	C₂×D₅	—	4	8	no	—
220	C₂×D₅	C₂²×C₃×C₄	1	2	yes	—
221	C₂×D₅	C₂²×C₃×C₄	1	4	yes	—
222	C₄×C₅	—	2	1	no	—
223	C₄×C₅	—	2	2	no	—
224	C₄×C₅	—	2	1	no	—
225	C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
226	Dic₅	—	2	1	no	—
227	Dic₅	—	2	2	no	—
228	Dic₅	—	2	1	no	—
229	Dic₅	C₂²×C₃×C₄	1	2	yes	—
230	C₂⁴	—	5	2	no	—
231	C₂×D₄	—	5	2	no	—
232	C₂×D₄	—	5	8	no	—
233	C₂×D₄	—	5	1	no	—
234	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic
235	C₂²×C₄	—	5	1	no	—
236	C₂²×C₄	—	5	2	no	—
237	C₂²×C₄	—	5	2	no	—
238	C₂²×C₄	—	5	2	no	—
239	C₂²×C₄	C₂×C₃×D₅	1	2	yes	complemented
240	C₄⋊C₄	—	5	1	no	—
241	C₄⋊C₄	—	5	1	no	—
242	C₄⋊C₄	—	5	1	no	—
243	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
244	C₂²⋊C₄	—	5	2	no	—
245	C₂²⋊C₄	—	5	2	no	—
246	C₂²⋊C₄	—	5	1	no	—
247	C₂²⋊C₄	—	5	1	no	—
248	C₂²⋊C₄	—	5	2	no	—
249	C₂²⋊C₄	—	5	2	no	—
250	C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
251	C₄²	—	5	2	no	—
252	C₄²	—	5	1	no	—
253	C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
254	C₃×C₅	#518	1	1	yes	characteristic, complemented, Hall
255	C₂²×C₃	—	2	2	no	—
256	C₂²×C₃	—	2	2	no	—
257	C₂²×C₃	—	5	2	no	—
258	C₂²×C₃	—	5	4	no	—
259	C₂²×C₃	—	10	2	no	—
260	C₂²×C₃	—	10	1	no	—
261	C₂²×C₃	—	10	2	no	—
262	C₂²×C₃	—	10	1	no	—
263	C₂²×C₃	—	20	8	no	—
264	C₂²×C₃	C₂×C₄×D₅	1	4	yes	—
265	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
266	C₃×C₄	—	2	1	no	—
267	C₃×C₄	—	2	2	no	—
268	C₃×C₄	—	2	1	no	—
269	C₃×C₄	—	5	2	no	—
270	C₃×C₄	—	10	1	no	—
271	C₃×C₄	—	10	2	no	—
272	C₃×C₄	—	10	1	no	—
273	C₃×C₄	C₂×C₄×D₅	1	2	yes	—
274	C₂×C₅	—	2	4	no	—
275	C₂×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
276	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
278	D₅	—	2	2	no	—
279	D₅	—	2	4	no	—
280	C₂³	—	5	1	no	—
281	C₂³	—	5	2	no	—
282	C₂³	—	5	8	no	—
283	C₂³	—	20	2	no	—
284	C₂³	—	20	2	no	—
285	C₂³	C₂²×C₃×D₅	1	2	yes	—
286	D₄	—	5	8	no	—
287	D₄	—	5	4	no	—
288	D₄	C₃×C₄×D₅	1	4	yes	complemented
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	5	1	no	—
291	C₂×C₄	—	5	4	no	—
292	C₂×C₄	—	5	1	no	—
293	C₂×C₄	—	5	2	no	—
294	C₂×C₄	—	5	1	no	—
295	C₂×C₄	—	20	2	no	—
296	C₂×C₄	—	20	2	no	—
297	C₂×C₄	—	20	2	no	—
298	C₂×C₄	C₂²×C₃×D₅	1	2	yes	—
299	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
300	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
302	C₂×C₃	—	2	4	no	—
303	C₂×C₃	—	10	2	no	—
304	C₂×C₃	—	10	4	no	—
305	C₂×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
306	C₂×C₃	#4144	1	1	yes	characteristic
307	C₂×C₃	#4149	1	1	yes	characteristic
308	C₅	C₃×#518	1	1	yes	characteristic, complemented, Sylow
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	5	2	no	—
312	C₂²	—	5	4	no	—
313	C₂²	—	10	2	no	—
314	C₂²	—	10	1	no	—
315	C₂²	—	10	2	no	—
316	C₂²	—	10	1	no	—
317	C₂²	—	20	8	no	—
318	C₂²	C₂×C₃×C₄×D₅	1	4	yes	—
319	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
320	C₄	—	2	1	no	—
321	C₄	—	2	2	no	—
322	C₄	—	2	1	no	—
323	C₄	—	5	2	no	—
324	C₄	—	10	1	no	—
325	C₄	—	10	2	no	—
326	C₄	—	10	1	no	—
327	C₄	C₂×C₃×C₄×D₅	1	2	yes	—
328	C₃	#65879	1	1	yes	characteristic, direct product factor, Sylow
329	C₂	—	2	4	no	—
330	C₂	—	10	2	no	—
331	C₂	—	10	4	no	—
332	C₂	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
333	C₂	C₃×#4144	1	1	yes	characteristic
334	C₂	C₃×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator	C₂×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂×C₃×D₄×D₅	C₂
cosocle	C₂²×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×D₄	D₅
hypocenter	C₅	C₃×#518
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×D₄×Dic₅	C₂	semidirect
4. C₃×C₄×C₂²⋊D₅	C₂	semidirect
5. C₂×C₃×#685	C₂	semidirect
6. C₃×#4039	C₂	semidirect
7. C₃×#4038	C₂	semidirect
8. C₃×#4027	C₂	semidirect
9. C₃×D₅×C₂²⋊C₄	C₂	semidirect
10. C₃×C₄×D₂₀	C₂	semidirect
11. C₃×#4018	C₂	semidirect
12. #65879	C₃	direct (N × H)
15. C₂²×C₃×C₄×C₅	C₂²	semidirect
17. C₂²×C₃×Dic₅	C₂²	semidirect
18. C₃×D₄×D₅	C₄	semidirect
21. C₂×C₃×C₄×D₅	C₂²	semidirect
22. C₂×C₃×C₄×D₅	C₂²	semidirect
23. C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₃×C₄²×C₅	C₂²	semidirect
26. C₃×C₂²⋊Dic₅	C₂²	semidirect
30. C₃×#685	C₂²	semidirect
31. C₃×#685	C₂²	semidirect
32. C₃×C₄⋊Dic₅	C₂²	semidirect
33. C₃×#683	C₂²	semidirect
34. C₃×#683	C₂²	semidirect
35. C₃×C₄×Dic₅	C₂²	semidirect
36. C₃×C₄×Dic₅	C₂²	semidirect
39. C₄×C₅×D₄	C₂×C₃	semidirect
40. D₄×Dic₅	C₂×C₃	semidirect
41. C₄×C₂²⋊D₅	C₂×C₃	semidirect
42. C₂×#685	C₂×C₃	semidirect
43. #4039	C₂×C₃	semidirect
44. #4038	C₂×C₃	semidirect
45. #4027	C₂×C₃	semidirect
46. D₅×C₂²⋊C₄	C₂×C₃	semidirect
47. C₄×D₂₀	C₂×C₃	semidirect
48. #4018	C₂×C₃	semidirect
52. C₂²×C₃×D₅	C₂×C₄	semidirect
55. C₃×C₅×D₄	C₂×C₄	semidirect
61. C₃×C₂²⋊D₅	C₂×C₄	semidirect
67. C₃×D₂₀	C₂×C₄	semidirect
70. C₃×C₄×D₅	C₂×C₄	semidirect
77. C₃×C₄×D₄	D₅	semidirect
84. C₂²×C₄×C₅	C₂²×C₃	semidirect
86. C₂²×Dic₅	C₂²×C₃	semidirect
87. D₄×D₅	C₃×C₄	semidirect
90. C₂×C₄×D₅	C₂²×C₃	semidirect
91. C₂×C₄×D₅	C₂²×C₃	semidirect
92. C₅×C₄⋊C₄	C₂²×C₃	semidirect
93. C₅×C₂²⋊C₄	C₂²×C₃	semidirect
94. C₄²×C₅	C₂²×C₃	semidirect
95. C₂²⋊Dic₅	C₂²×C₃	semidirect
99. #685	C₂²×C₃	semidirect
100. #685	C₂²×C₃	semidirect
101. C₄⋊Dic₅	C₂²×C₃	semidirect
102. #683	C₂²×C₃	semidirect
103. #683	C₂²×C₃	semidirect
104. C₄×Dic₅	C₂²×C₃	semidirect
105. C₄×Dic₅	C₂²×C₃	semidirect
135. C₂²×C₃×C₄	C₂×D₅	semidirect
139. C₃×C₄⋊C₄	C₂×D₅	semidirect
146. C₃×C₂²⋊C₄	C₂×D₅	semidirect
149. C₃×C₄²	C₂×D₅	semidirect
153. C₂²×D₅	C₂×C₃×C₄	semidirect
156. C₅×D₄	C₂×C₃×C₄	semidirect
162. C₂²⋊D₅	C₂×C₃×C₄	semidirect
168. D₂₀	C₂×C₃×C₄	semidirect
171. C₄×D₅	C₂×C₃×C₄	semidirect
178. C₄×D₄	C₃×D₅	semidirect
197. C₃×D₄	C₄×D₅	semidirect
239. C₂²×C₄	C₂×C₃×D₅	semidirect
243. C₄⋊C₄	C₂×C₃×D₅	semidirect
250. C₂²⋊C₄	C₂×C₃×D₅	semidirect
253. C₄²	C₂×C₃×D₅	semidirect
254. C₃×C₅	#518	semidirect
288. D₄	C₃×C₄×D₅	semidirect
308. C₅	C₃×#518	semidirect
328. C₃	#65879	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×D₄×D₅	2
C₃×C₄×C₅×D₄	2
C₃×D₄×Dic₅	2
C₃×C₄×C₂²⋊D₅	2
C₂×C₃×#685	2
C₃×#4039	2
C₃×#4038	2
C₃×#4027	2
C₃×D₅×C₂²⋊C₄	2
C₃×C₄×D₂₀	2
C₃×#4018	2
#65879	3
C₃×#518	5

Subgroups — C3×#65879 #11755556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65879 #11755556