Subgroups — C₅×#68363 #14284074

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₅×#4707	C₂	1	1	yes	maximal, characteristic
3	C₅×#4705	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4543	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4465	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1528	—	3	1	no	maximal, Hall
9	C₃×C₅×#125	C₂²	1	1	yes	characteristic
10	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
11	C₅×D₃×C₄⋊C₄	—	2	1	no	—
12	C₅×D₃×C₄⋊C₄	—	2	1	no	—
13	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
15	C₅×#890	C₄	1	1	yes	characteristic
16	C₅×#890	C₄	1	1	yes	characteristic
17	C₅×#889	—	2	1	no	—
18	C₅×#889	—	2	1	no	—
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₅×#870	C₂²	1	1	yes	characteristic
21	C₃×C₅×#97	C₂²	1	1	yes	characteristic
22	C₃×C₅×#97	C₂²	1	1	yes	characteristic
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	C₅×#803	C₂²	1	1	yes	characteristic
27	C₅×#803	C₂²	1	1	yes	characteristic
28	#68363	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#125	—	3	1	no	—
30	C₅×#432	—	3	1	no	—
31	C₄×C₅×M₁₆	—	3	1	no	—
32	C₅×#330	—	3	1	no	—
33	C₅×#330	—	3	1	no	—
34	C₅×#330	—	3	1	no	—
35	C₅×#330	D₃	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×D₃	—	2	1	no	—
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
40	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	—	2	1	no	—
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₅×C₄⋊Dic₃	—	2	1	no	—
49	C₅×C₄⋊Dic₃	—	2	1	no	—
50	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₅×Dic₃⋊C₄	—	2	1	no	—
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
64	D₃×#125	C₂×C₅	1	1	yes	characteristic
65	#4707	C₂×C₅	1	1	yes	characteristic
66	#4705	C₂×C₅	1	1	yes	characteristic
67	C₃×#330	C₂×C₅	1	1	yes	characteristic, complemented
68	#4543	C₂×C₅	1	1	yes	characteristic, complemented
69	#4465	C₂×C₅	1	1	yes	characteristic, complemented
70	#4465	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₅×M₁₆	—	6	1	no	—
72	C₅×#125	—	3	1	no	—
73	C₅×#125	—	3	1	no	—
74	C₅×#125	—	3	1	no	—
75	C₅×#125	—	6	1	no	—
76	C₅×#125	—	6	1	no	—
77	C₅×#125	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	—	3	1	no	—
79	C₂×C₅×C₄⋊C₄	—	3	1	no	—
80	C₂×C₅×C₄⋊C₄	—	6	1	no	—
81	C₂×C₅×C₄⋊C₄	—	6	1	no	—
82	C₂×C₄²×C₅	—	3	1	no	—
83	C₅×C₄⋊C₈	—	6	1	no	—
84	C₅×C₂²⋊C₈	—	6	1	no	—
85	C₅×#97	—	3	1	no	—
86	C₅×#97	—	3	1	no	—
87	C₅×#97	C₂×D₃	1	1	yes	characteristic
88	C₅×#97	C₂×D₃	1	1	yes	characteristic
89	C₄×C₅×C₈	—	6	1	no	—
90	#1528	—	3	1	no	Sylow
91	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₅×Dic₃	—	2	1	no	—
98	C₂×C₅×Dic₃	—	2	1	no	—
99	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₄×C₅×D₃	—	2	2	no	—
103	C₄×C₅×D₃	—	2	2	no	—
104	C₄×C₅×D₃	—	4	1	no	—
105	C₄×C₅×D₃	—	4	2	no	—
106	C₄×C₅×D₃	—	4	2	no	—
107	C₃×C₅×C₈	—	2	2	no	—
108	C₃×C₅×C₈	—	4	1	no	—
109	C₅×C₃⋊C₈	—	2	2	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₃×#125	C₂²×C₅	1	1	yes	characteristic
112	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
113	D₃×C₄⋊C₄	—	2	1	no	—
114	D₃×C₄⋊C₄	—	2	1	no	—
115	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
116	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
117	#890	C₄×C₅	1	1	yes	characteristic
118	#890	C₄×C₅	1	1	yes	characteristic
119	#889	—	2	1	no	—
120	#889	—	2	1	no	—
121	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
122	#870	C₂²×C₅	1	1	yes	characteristic
123	C₃×#97	C₂²×C₅	1	1	yes	characteristic
124	C₃×#97	C₂²×C₅	1	1	yes	characteristic
125	(C₂×D₃)⋊C₈	—	2	1	no	—
126	Dic₃⋊C₈	—	2	1	no	—
127	C₈×Dic₃	—	2	1	no	—
128	#803	C₂²×C₅	1	1	yes	characteristic
129	#803	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄×C₅	—	3	1	no	—
131	C₂²×C₄×C₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	3	1	no	—
133	C₂²×C₄×C₅	—	6	1	no	—
134	C₂²×C₄×C₅	—	6	1	no	—
135	C₅×M₁₆	—	6	4	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	6	1	no	—
139	C₂×C₅×C₈	—	6	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	3	1	no	—
143	C₅×C₄⋊C₄	—	3	1	no	—
144	C₅×C₄⋊C₄	—	6	1	no	—
145	C₅×C₄⋊C₄	—	6	1	no	—
146	C₅×C₄⋊C₄	—	6	1	no	—
147	C₅×C₄⋊C₄	—	6	1	no	—
148	C₅×C₄⋊C₄	—	6	1	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₄⋊C₄	—	6	1	no	—
151	C₅×C₄⋊C₄	—	6	1	no	—
152	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
154	C₄²×C₅	—	3	1	no	—
155	C₄²×C₅	—	3	1	no	—
156	C₄²×C₅	—	3	1	no	—
157	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂×#125	—	3	1	no	—
159	#432	—	3	1	no	—
160	C₄×M₁₆	—	3	1	no	—
161	#330	—	3	1	no	—
162	#330	—	3	1	no	—
163	#330	—	3	1	no	—
164	#330	C₅×D₃	1	1	yes	characteristic, complemented
165	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₅×D₃	—	2	1	no	—
167	C₂×C₅×D₃	—	2	1	no	—
168	C₂×C₅×D₃	#104	1	2	yes	—
169	C₃×C₄×C₅	—	2	1	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	2	1	no	—
172	C₃×C₄×C₅	—	4	1	no	—
173	C₃×C₄×C₅	—	4	1	no	—
174	C₅×Dic₃	—	2	1	no	—
175	C₅×Dic₃	—	2	1	no	—
176	C₅×Dic₃	—	4	1	no	—
177	C₅×Dic₃	—	4	1	no	—
178	C₅×Dic₃	#101	1	2	yes	—
179	C₂×C₄×D₃	—	2	1	no	—
180	C₂×C₄×D₃	—	2	1	no	—
181	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
183	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
184	C₂×C₃×C₈	—	2	1	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
190	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
191	C₄⋊Dic₃	—	2	1	no	—
192	C₄⋊Dic₃	—	2	1	no	—
193	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
194	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
195	Dic₃⋊C₄	—	2	1	no	—
196	Dic₃⋊C₄	—	2	1	no	—
197	Dic₃⋊C₄	—	2	1	no	—
198	Dic₃⋊C₄	—	2	1	no	—
199	Dic₃⋊C₄	—	2	1	no	—
200	Dic₃⋊C₄	—	2	1	no	—
201	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
202	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
203	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
204	C₂×C₃⋊C₈	—	2	1	no	—
205	C₂×C₃⋊C₈	—	2	1	no	—
206	ΓL(1,𝔽₂₅)	—	2	4	no	—
207	C₂³×C₅	—	3	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	3	1	no	—
211	C₂×C₄×C₅	—	3	1	no	—
212	C₂×C₄×C₅	—	3	1	no	—
213	C₂×C₄×C₅	—	6	2	no	—
214	C₂×C₄×C₅	—	6	2	no	—
215	C₂×C₄×C₅	—	6	1	no	—
216	C₂×C₄×C₅	—	6	1	no	—
217	C₂×C₄×C₅	—	12	1	no	—
218	C₂×C₄×C₅	—	12	2	no	—
219	C₂×C₄×C₅	—	12	2	no	—
220	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
221	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	4	1	no	—
225	C₅×C₈	—	6	2	no	—
226	C₅×C₈	—	12	1	no	—
227	C₂×M₁₆	—	6	1	no	—
228	#125	—	3	1	no	—
229	#125	—	3	1	no	—
230	#125	—	3	1	no	—
231	#125	—	6	1	no	—
232	#125	—	6	1	no	—
233	#125	C₂×C₅×D₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	—	3	1	no	—
235	C₂×C₄⋊C₄	—	3	1	no	—
236	C₂×C₄⋊C₄	—	6	1	no	—
237	C₂×C₄⋊C₄	—	6	1	no	—
238	C₂×C₄²	—	3	1	no	—
239	C₄⋊C₈	—	6	1	no	—
240	C₂²⋊C₈	—	6	1	no	—
241	#97	—	3	1	no	—
242	#97	—	3	1	no	—
243	#97	C₂×C₅×D₃	1	1	yes	characteristic
244	#97	C₂×C₅×D₃	1	1	yes	characteristic
245	C₄×C₈	—	6	1	no	—
246	C₂×C₃×C₅	C₂×#101	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
248	C₂×C₃×C₅	#421	1	1	yes	characteristic
249	C₅×D₃	—	2	2	no	—
250	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂×Dic₃	—	2	1	no	—
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₄×D₃	—	2	2	no	—
262	C₄×D₃	—	2	2	no	—
263	C₄×D₃	—	4	1	no	—
264	C₄×D₃	—	4	2	no	—
265	C₄×D₃	—	4	2	no	—
266	C₃×C₈	—	2	2	no	—
267	C₃×C₈	—	4	1	no	—
268	C₃⋊C₈	—	2	2	no	—
269	C₃⋊C₈	—	4	1	no	—
270	C₂²×C₅	—	3	2	no	—
271	C₂²×C₅	—	6	1	no	—
272	C₂²×C₅	—	6	1	no	—
273	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	3	2	no	—
278	C₄×C₅	—	4	1	no	—
279	C₄×C₅	—	4	1	no	—
280	C₄×C₅	—	6	1	no	—
281	C₄×C₅	—	6	1	no	—
282	C₄×C₅	—	12	1	no	—
283	C₄×C₅	—	12	1	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	—	3	1	no	—
286	C₂²×C₄	—	3	1	no	—
287	C₂²×C₄	—	6	1	no	—
288	C₂²×C₄	—	6	1	no	—
289	M₁₆	—	6	4	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	6	1	no	—
293	C₂×C₈	—	6	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	3	1	no	—
297	C₄⋊C₄	—	3	1	no	—
298	C₄⋊C₄	—	6	1	no	—
299	C₄⋊C₄	—	6	1	no	—
300	C₄⋊C₄	—	6	1	no	—
301	C₄⋊C₄	—	6	1	no	—
302	C₄⋊C₄	—	6	1	no	—
303	C₄⋊C₄	—	6	1	no	—
304	C₄⋊C₄	—	6	1	no	—
305	C₄⋊C₄	—	6	1	no	—
306	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
307	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
308	C₄²	—	3	1	no	—
309	C₄²	—	3	1	no	—
310	C₄²	—	3	1	no	—
311	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
312	C₃×C₅	#1528	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×D₃	—	2	1	no	—
315	C₂×D₃	—	2	1	no	—
316	C₂×D₃	C₅×#104	1	2	yes	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	4	1	no	—
321	C₃×C₄	—	4	1	no	—
322	Dic₃	—	2	1	no	—
323	Dic₃	—	2	1	no	—
324	Dic₃	—	4	1	no	—
325	Dic₃	—	4	1	no	—
326	Dic₃	C₅×#101	1	2	yes	—
327	C₂×C₅	—	6	2	no	—
328	C₂×C₅	D₃×#101	1	1	yes	characteristic
329	C₂×C₅	D₃×#104	1	1	yes	characteristic
330	C₂×C₅	#4821	1	1	yes	characteristic
331	C₂³	—	3	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	3	1	no	—
335	C₂×C₄	—	3	1	no	—
336	C₂×C₄	—	3	1	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	6	2	no	—
339	C₂×C₄	—	6	1	no	—
340	C₂×C₄	—	6	1	no	—
341	C₂×C₄	—	12	1	no	—
342	C₂×C₄	—	12	2	no	—
343	C₂×C₄	—	12	2	no	—
344	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
345	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
346	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	4	1	no	—
349	C₈	—	6	2	no	—
350	C₈	—	12	1	no	—
351	C₂×C₃	C₂×C₅×#101	1	1	yes	characteristic
352	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
353	C₂×C₃	C₅×#421	1	1	yes	characteristic
354	D₃	—	2	2	no	—
355	C₅	#68363	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²	—	3	2	no	—
357	C₂²	—	6	1	no	—
358	C₂²	—	6	1	no	—
359	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	3	2	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	6	1	no	—
367	C₄	—	6	1	no	—
368	C₄	—	12	1	no	—
369	C₄	—	12	1	no	—
370	C₃	C₅×#1528	1	1	yes	characteristic, complemented, Sylow
371	C₂	—	6	2	no	—
372	C₂	C₅×D₃×#101	1	1	yes	characteristic
373	C₂	C₅×D₃×#104	1	1	yes	characteristic
374	C₂	C₅×#4821	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#330	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×D₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#330	D₃
hypocenter	C₃	C₅×#1528
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#330

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#330	C₂	semidirect
5. C₅×#4543	C₂	semidirect
6. C₅×#4465	C₂	semidirect
7. C₅×#4465	C₂	semidirect
28. #68363	C₅	direct (N × H)
35. C₅×#330	D₃	semidirect
67. C₃×#330	C₂×C₅	semidirect
68. #4543	C₂×C₅	semidirect
69. #4465	C₂×C₅	semidirect
70. #4465	C₂×C₅	semidirect
164. #330	C₅×D₃	semidirect
312. C₃×C₅	#1528	semidirect
355. C₅	#68363	direct (N × H)
370. C₃	C₅×#1528	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×#125	2
C₅×#4707	2
C₅×#4705	2
C₃×C₅×#330	2
C₅×#4543	2
C₅×#4465	2
C₅×#1528	3
#68363	5

Subgroups — C5×#68363 #14284074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68363 #14284074