Subgroups — C₃×#10604559 #14306000

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66002	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4010	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4008	C₂	1	2	yes	maximal, complemented
4	C₃×C₄²×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65682	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604559	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×#713	C₂²	1	1	yes	characteristic
8	C₂×C₃×#711	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
10	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
11	C₂×C₃×#700	C₂²	1	2	yes	—
12	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
13	C₃×#4090	C₄	1	1	yes	characteristic, complemented
14	C₃×#4086	C₄	1	1	yes	characteristic, complemented
15	C₃×#4030	—	2	2	no	—
16	C₃×#4027	—	2	2	no	—
17	C₃×#4021	C₄	1	1	yes	characteristic, complemented
18	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
19	C₃×#4010	—	2	4	no	—
20	C₃×#4008	—	2	4	no	—
21	C₃×#4004	—	2	2	no	—
22	C₃×#1962	—	5	1	no	maximal, Hall
23	#66002	C₂×C₃	1	1	yes	characteristic
24	C₂×#4010	C₂×C₃	1	2	yes	complemented
25	C₂×#4008	C₂×C₃	1	2	yes	complemented
26	C₄²×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
27	#65682	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
29	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
32	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
33	C₂²×C₃×Dic₅	—	2	1	no	—
34	C₃×#713	—	2	2	no	—
35	C₃×#713	—	2	2	no	—
36	C₃×#711	—	2	2	no	—
37	C₃×#711	—	2	2	no	—
38	C₂×C₃×D₂₀	—	2	1	no	—
39	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	—	2	1	no	—
41	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
42	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×#170	—	2	2	no	—
45	C₃×C₄×AGL(1,𝔽₅)	—	2	8	no	—
46	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
47	C₃×C₄×AGL(1,𝔽₅)	D₄	1	4	yes	complemented
48	C₃×#700	—	2	2	no	—
49	C₃×#700	—	2	2	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×#685	—	2	2	no	—
53	C₃×#683	—	2	2	no	—
54	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄×Dic₅	D₄	1	2	yes	—
56	C₃×#532	—	5	1	no	—
57	C₃×#423	—	5	1	no	—
58	C₂×C₃×#104	—	5	2	no	—
59	C₂×C₃×#104	—	5	2	no	—
60	C₃×C₄³	—	5	1	no	—
61	C₂×#713	C₂²×C₃	1	1	yes	characteristic
62	C₂×#711	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
64	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
65	C₂×#700	C₂²×C₃	1	2	yes	—
66	C₅×#124	C₃×C₄	1	1	yes	characteristic, complemented
67	#4090	C₃×C₄	1	1	yes	characteristic, complemented
68	#4086	C₃×C₄	1	1	yes	characteristic, complemented
69	#4030	—	2	2	no	—
70	#4027	—	2	2	no	—
71	#4021	C₃×C₄	1	1	yes	characteristic, complemented
72	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
73	#4010	—	2	4	no	—
74	#4008	—	2	4	no	—
75	#4004	—	2	2	no	—
76	#1962	—	5	1	no	Sylow
77	C₂³×C₃×C₅	—	2	1	no	—
78	C₂²×C₃×D₅	—	2	1	no	—
79	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
81	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
82	C₃×C₅×Q₈	—	2	2	no	—
83	C₃×C₅×D₄	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₃×C₂²⋊D₅	—	4	2	no	—
88	C₃×C₂²⋊D₅	—	4	4	no	—
89	C₂×C₃×Dic₅	—	2	1	no	—
90	C₂×C₃×Dic₅	—	4	1	no	—
91	C₂×C₃×Dic₅	—	4	1	no	—
92	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
94	C₃×D₂₀	—	2	2	no	—
95	C₃×D₂₀	—	4	2	no	—
96	C₃×C₄×D₅	—	2	4	no	—
97	C₃×C₄×D₅	—	4	1	no	—
98	C₃×C₄×D₅	—	4	1	no	—
99	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
100	C₃×C₄×D₅	#41	1	2	yes	—
101	C₃×Dic₁₀	—	2	2	no	—
102	C₃×#170	—	4	2	no	—
103	C₂×C₃×#41	—	5	1	no	—
104	C₂×C₃×#41	—	5	1	no	—
105	C₂×C₃×M₁₆	—	5	2	no	—
106	C₃×C₄⋊Q₈	—	5	1	no	—
107	C₃×#127	—	5	1	no	—
108	C₃×#124	—	5	1	no	—
109	C₃×#124	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
110	C₃×#121	—	10	2	no	—
111	C₃×C₄×D₄	—	10	2	no	—
112	C₂×C₃×C₄²	—	5	1	no	—
113	C₂×C₃×C₄²	—	5	2	no	—
114	C₂×C₃×C₄²	—	10	2	no	—
115	C₃×C₄⋊C₈	—	10	2	no	—
116	C₃×#104	—	10	4	no	—
117	C₃×#104	—	10	4	no	—
118	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
119	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₅	—	2	1	no	—
122	C₂×C₂²⋊D₅	—	2	2	no	—
123	C₂²×Dic₅	—	2	1	no	—
124	#713	—	2	2	no	—
125	#713	—	2	2	no	—
126	#711	—	2	2	no	—
127	#711	—	2	2	no	—
128	C₂×D₂₀	—	2	1	no	—
129	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂×C₄×D₅	—	2	1	no	—
131	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
132	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
133	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂×#170	—	2	2	no	—
135	C₄×AGL(1,𝔽₅)	—	2	8	no	—
136	C₄×AGL(1,𝔽₅)	—	2	2	no	—
137	C₄×AGL(1,𝔽₅)	C₃×D₄	1	4	yes	complemented
138	#700	—	2	2	no	—
139	#700	—	2	2	no	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
142	#685	—	2	2	no	—
143	#683	—	2	2	no	—
144	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
145	C₄×Dic₅	C₃×D₄	1	2	yes	—
146	#532	—	5	1	no	—
147	#423	—	5	1	no	—
148	C₂×#104	—	5	2	no	—
149	C₂×#104	—	5	2	no	—
150	C₄³	—	5	1	no	—
151	C₂²×C₃×C₅	—	4	1	no	—
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₃×D₅	—	2	2	no	—
155	C₂×C₃×D₅	—	4	1	no	—
156	C₂×C₃×D₅	—	4	2	no	—
157	C₂×C₃×D₅	#121	1	2	yes	—
158	C₃×AGL(1,𝔽₅)	—	2	8	no	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	—	4	1	no	—
161	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
162	C₃×Dic₅	—	4	1	no	—
163	C₃×Dic₅	#104	1	4	yes	complemented
164	C₃×Dic₅	#124	1	1	yes	characteristic
165	C₃×Dic₅	#127	1	1	yes	characteristic
166	C₃×#41	—	10	2	no	—
167	C₃×#41	—	10	2	no	—
168	C₃×#41	—	10	2	no	—
169	C₃×#41	—	10	2	no	—
170	C₂×C₃×Q₈	—	5	1	no	—
171	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
172	C₂×C₃×D₄	—	5	1	no	—
173	C₂×C₃×D₄	—	10	1	no	—
174	C₂×C₃×D₄	—	10	2	no	—
175	C₂×C₃×D₄	—	10	1	no	—
176	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	2	no	—
179	C₂²×C₃×C₄	—	10	1	no	—
180	C₂²×C₃×C₄	—	10	1	no	—
181	C₂²×C₃×C₄	—	10	2	no	—
182	C₃×M₁₆	—	10	2	no	—
183	C₃×M₁₆	—	10	2	no	—
184	C₂×C₃×C₈	—	10	2	no	—
185	C₃×C₄⋊C₄	—	10	2	no	—
186	C₃×C₂²⋊C₄	—	2	2	no	—
187	C₃×C₂²⋊C₄	—	10	2	no	—
188	C₃×C₄²	—	5	2	no	—
189	C₃×C₄²	—	5	1	no	—
190	C₃×C₄²	—	5	4	no	—
191	C₃×C₄²	—	10	2	no	—
192	C₃×C₄²	—	10	8	no	—
193	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
194	C₂³×C₅	—	2	1	no	—
195	C₂²×D₅	—	2	1	no	—
196	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
197	C₂×AGL(1,𝔽₅)	—	2	8	no	—
198	C₂×AGL(1,𝔽₅)	—	2	4	no	—
199	C₅×Q₈	—	2	2	no	—
200	C₅×D₄	—	2	2	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
204	C₂²⋊D₅	—	4	2	no	—
205	C₂²⋊D₅	—	4	4	no	—
206	C₂×Dic₅	—	2	1	no	—
207	C₂×Dic₅	—	4	1	no	—
208	C₂×Dic₅	—	4	1	no	—
209	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
210	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
211	D₂₀	—	2	2	no	—
212	D₂₀	—	4	2	no	—
213	C₄×D₅	—	2	4	no	—
214	C₄×D₅	—	4	1	no	—
215	C₄×D₅	—	4	1	no	—
216	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
217	C₄×D₅	C₃×#41	1	2	yes	—
218	Dic₁₀	—	2	2	no	—
219	#170	—	4	2	no	—
220	C₂×#41	—	5	1	no	—
221	C₂×#41	—	5	1	no	—
222	C₂×M₁₆	—	5	2	no	—
223	C₄⋊Q₈	—	5	1	no	—
224	#127	—	5	1	no	—
225	#124	—	5	1	no	—
226	#124	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
227	#121	—	10	2	no	—
228	C₄×D₄	—	10	2	no	—
229	C₂×C₄²	—	5	1	no	—
230	C₂×C₄²	—	5	2	no	—
231	C₂×C₄²	—	10	2	no	—
232	C₄⋊C₈	—	10	2	no	—
233	#104	—	10	4	no	—
234	#104	—	10	4	no	—
235	C₂×C₃×C₅	—	8	1	no	—
236	C₂×C₃×C₅	#390	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂×#104	1	2	yes	—
238	C₃×D₅	—	2	2	no	—
239	C₃×D₅	—	8	1	no	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	—	5	1	no	—
242	C₂³×C₃	—	10	1	no	—
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	10	2	no	—
245	C₃×D₄	—	2	2	no	—
246	C₃×D₄	—	10	2	no	—
247	C₃×D₄	—	20	2	no	—
248	C₃×D₄	—	20	4	no	—
249	C₃×D₄	—	20	2	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	5	2	no	—
252	C₂×C₃×C₄	—	5	1	no	—
253	C₂×C₃×C₄	—	5	2	no	—
254	C₂×C₃×C₄	—	5	2	no	—
255	C₂×C₃×C₄	—	10	4	no	—
256	C₂×C₃×C₄	—	10	4	no	—
257	C₂×C₃×C₄	—	10	8	no	—
258	C₂×C₃×C₄	—	10	1	no	—
259	C₂×C₃×C₄	—	20	1	no	—
260	C₂×C₃×C₄	—	20	1	no	—
261	C₂×C₃×C₄	—	20	1	no	—
262	C₂×C₃×C₄	—	20	1	no	—
263	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
264	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
265	C₃×C₈	—	20	2	no	—
266	C₂²×C₅	—	4	1	no	—
267	C₂²×C₅	—	4	2	no	—
268	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×D₅	—	2	2	no	—
270	C₂×D₅	—	4	1	no	—
271	C₂×D₅	—	4	2	no	—
272	C₂×D₅	C₃×#121	1	2	yes	—
273	AGL(1,𝔽₅)	—	2	8	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	4	1	no	—
276	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
277	Dic₅	—	4	1	no	—
278	Dic₅	C₃×#104	1	4	yes	complemented
279	Dic₅	C₃×#124	1	1	yes	characteristic
280	Dic₅	C₃×#127	1	1	yes	characteristic
281	#41	—	10	2	no	—
282	#41	—	10	2	no	—
283	#41	—	10	2	no	—
284	#41	—	10	2	no	—
285	C₂×Q₈	—	5	1	no	—
286	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
287	C₂×D₄	—	5	1	no	—
288	C₂×D₄	—	10	1	no	—
289	C₂×D₄	—	10	2	no	—
290	C₂×D₄	—	10	1	no	—
291	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	5	2	no	—
294	C₂²×C₄	—	10	1	no	—
295	C₂²×C₄	—	10	1	no	—
296	C₂²×C₄	—	10	2	no	—
297	M₁₆	—	10	2	no	—
298	M₁₆	—	10	2	no	—
299	C₂×C₈	—	10	2	no	—
300	C₄⋊C₄	—	10	2	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	10	2	no	—
303	C₄²	—	5	2	no	—
304	C₄²	—	5	1	no	—
305	C₄²	—	5	4	no	—
306	C₄²	—	10	2	no	—
307	C₄²	—	10	8	no	—
308	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
309	C₃×C₅	#1962	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	4	2	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	—	5	2	no	—
313	C₂²×C₃	—	10	2	no	—
314	C₂²×C₃	—	20	2	no	—
315	C₂²×C₃	—	20	1	no	—
316	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	5	4	no	—
320	C₃×C₄	—	5	1	no	—
321	C₃×C₄	—	5	1	no	—
322	C₃×C₄	—	10	8	no	—
323	C₃×C₄	—	20	1	no	—
324	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
325	C₂×C₅	—	8	1	no	—
326	C₂×C₅	C₃×#390	1	1	yes	characteristic
327	C₂×C₅	C₂×C₃×#104	1	2	yes	—
328	D₅	—	2	2	no	—
329	D₅	—	8	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	5	1	no	—
332	C₂³	—	10	1	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	10	2	no	—
335	D₄	—	2	2	no	—
336	D₄	—	10	2	no	—
337	D₄	—	20	2	no	—
338	D₄	—	20	4	no	—
339	D₄	—	20	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	5	2	no	—
342	C₂×C₄	—	5	1	no	—
343	C₂×C₄	—	5	2	no	—
344	C₂×C₄	—	5	2	no	—
345	C₂×C₄	—	10	4	no	—
346	C₂×C₄	—	10	4	no	—
347	C₂×C₄	—	10	8	no	—
348	C₂×C₄	—	10	1	no	—
349	C₂×C₄	—	20	1	no	—
350	C₂×C₄	—	20	1	no	—
351	C₂×C₄	—	20	1	no	—
352	C₂×C₄	—	20	1	no	—
353	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
354	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₈	—	20	2	no	—
356	C₂×C₃	—	8	1	no	—
357	C₂×C₃	—	10	2	no	—
358	C₂×C₃	—	40	1	no	—
359	C₂×C₃	#65780	1	1	yes	characteristic
360	C₂×C₃	D₅⋊#104	1	2	yes	—
361	C₅	C₃×#1962	1	1	yes	characteristic, complemented, Sylow
362	C₂²	—	4	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	5	2	no	—
365	C₂²	—	10	2	no	—
366	C₂²	—	20	1	no	—
367	C₂²	—	20	2	no	—
368	C₂²	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	5	1	no	—
372	C₄	—	5	1	no	—
373	C₄	—	5	4	no	—
374	C₄	—	10	8	no	—
375	C₄	—	20	1	no	—
376	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
377	C₃	#10604559	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	8	1	no	—
379	C₂	—	10	2	no	—
380	C₂	—	40	1	no	—
381	C₂	C₃×#65780	1	1	yes	characteristic
382	C₂	C₃×D₅⋊#104	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#124	C₄
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×#66002	C₂
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₃×#124	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1962
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#124

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4010	C₂	semidirect
3. C₂×C₃×#4008	C₂	semidirect
4. C₃×C₄²×AGL(1,𝔽₅)	C₂	semidirect
5. C₃×#65682	C₂	semidirect
6. #10604559	C₃	direct (N × H)
12. C₃×C₅×#124	C₄	semidirect
13. C₃×#4090	C₄	semidirect
14. C₃×#4086	C₄	semidirect
17. C₃×#4021	C₄	semidirect
24. C₂×#4010	C₂×C₃	semidirect
25. C₂×#4008	C₂×C₃	semidirect
26. C₄²×AGL(1,𝔽₅)	C₂×C₃	semidirect
27. #65682	C₂×C₃	semidirect
47. C₃×C₄×AGL(1,𝔽₅)	D₄	semidirect
66. C₅×#124	C₃×C₄	semidirect
67. #4090	C₃×C₄	semidirect
68. #4086	C₃×C₄	semidirect
71. #4021	C₃×C₄	semidirect
109. C₃×#124	AGL(1,𝔽₅)	semidirect
137. C₄×AGL(1,𝔽₅)	C₃×D₄	semidirect
163. C₃×Dic₅	#104	semidirect
226. #124	C₃×AGL(1,𝔽₅)	semidirect
278. Dic₅	C₃×#104	semidirect
309. C₃×C₅	#1962	semidirect
361. C₅	C₃×#1962	semidirect
377. C₃	#10604559	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#66002	2
C₂×C₃×#4010	2
C₂×C₃×#4008	2
C₃×C₄²×AGL(1,𝔽₅)	2
C₃×#65682	2
#10604559	3
C₃×#1962	5

Subgroups — C3×#10604559 #14306000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604559 #14306000