Subgroups — C₅×#71061 #14290000

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5577	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1641	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	—	2	1	no	—
10	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₅×#895	—	2	2	no	—
14	C₅×#895	—	2	1	no	—
15	C₅×#874	—	2	1	no	—
16	C₅×#874	C₂²	1	1	yes	characteristic
17	C₄×C₅×D₁₂	—	2	1	no	—
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#103	—	2	1	no	—
21	C₅×#809	—	2	1	no	—
22	C₅×#809	—	2	2	no	—
23	C₅×#807	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	#71061	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#550	—	3	1	no	—
28	C₅×#486	—	3	1	no	—
29	C₅×#474	—	3	1	no	—
30	C₅×#462	D₃	1	1	yes	characteristic, complemented
31	C₅×#331	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
36	C₅×#239	—	4	2	no	—
37	C₅×#239	—	4	2	no	—
38	C₂×C₅×D₁₂	—	2	2	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	2	no	—
42	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
43	C₂×C₅×D₁₂	D₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	—	2	2	no	—
45	C₂×C₄×C₅×D₃	—	2	1	no	—
46	C₃×C₅×Q₁₆	—	4	2	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	—	2	1	no	—
53	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
55	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
56	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	#5577	C₂×C₅	1	1	yes	characteristic
60	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
61	#5088	C₂×C₅	1	1	yes	characteristic, complemented
62	#5087	C₂×C₅	1	1	yes	characteristic, complemented
63	#4535	C₂×C₅	1	1	yes	characteristic, complemented
64	#4485	C₂×C₅	1	1	yes	characteristic, complemented
65	#4483	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	—	6	1	no	—
67	C₂×C₅×Q₁₆	—	2	1	no	—
68	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
69	C₅×#127	—	3	1	no	—
70	C₅×#127	—	6	1	no	—
71	C₅×#121	—	6	2	no	—
72	C₅×#121	—	6	1	no	—
73	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
74	C₄×C₅×D₄	—	3	1	no	—
75	C₄×C₅×D₄	—	6	1	no	—
76	C₅×#107	—	6	1	no	—
77	C₅×C₄⋊C₈	—	3	1	no	—
78	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
79	C₅×#103	—	2	1	no	—
80	C₅×#102	—	6	1	no	—
81	C₅×#102	—	6	2	no	—
82	C₄×C₅×C₈	—	3	1	no	—
83	#1641	—	3	1	no	Sylow
84	C₂²×C₅×D₃	—	2	1	no	—
85	C₂²×C₅×D₃	—	2	2	no	—
86	C₃×C₅×Q₈	—	2	1	no	—
87	C₃×C₅×Q₈	—	4	1	no	—
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×Q₈	D₈	1	2	yes	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₅×Dic₃	—	2	1	no	—
97	C₅×D₁₂	—	2	1	no	—
98	C₅×D₁₂	—	2	1	no	—
99	C₅×D₁₂	—	4	4	no	—
100	C₅×D₁₂	—	4	2	no	—
101	C₅×D₁₂	—	4	1	no	—
102	C₅×D₁₂	—	4	1	no	—
103	C₅×D₁₂	—	4	1	no	—
104	C₅×D₁₂	—	4	1	no	—
105	C₅×D₁₂	—	8	2	no	—
106	C₄×C₅×D₃	—	4	4	no	—
107	C₄×C₅×D₃	—	4	1	no	—
108	C₄×C₅×D₃	—	4	1	no	—
109	C₃×C₅×C₈	—	4	1	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₅×C₃⋊C₈	—	4	1	no	—
112	C₂×#239	—	2	1	no	—
113	C₂×C₃×Q₁₆	—	2	1	no	—
114	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
115	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
116	#895	—	2	2	no	—
117	#895	—	2	1	no	—
118	#874	—	2	1	no	—
119	#874	C₂²×C₅	1	1	yes	characteristic
120	C₄×D₁₂	—	2	1	no	—
121	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
122	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
123	C₃×#103	—	2	1	no	—
124	#809	—	2	1	no	—
125	#809	—	2	2	no	—
126	#807	—	2	1	no	—
127	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
128	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
129	C₅×#41	—	12	2	no	—
130	C₅×#41	—	12	2	no	—
131	C₂×C₅×Q₈	—	2	1	no	—
132	C₂×C₅×Q₈	#67	1	1	yes	characteristic
133	C₂×C₅×D₄	—	3	1	no	—
134	C₂×C₅×D₄	—	3	2	no	—
135	C₂×C₅×D₄	—	6	2	no	—
136	C₂×C₅×D₄	—	6	2	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂×C₅×D₄	—	6	1	no	—
139	C₂²×C₄×C₅	—	6	2	no	—
140	C₂²×C₄×C₅	—	6	1	no	—
141	C₅×Q₁₆	—	4	2	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	3	1	no	—
149	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
150	C₅×C₂²⋊C₄	—	6	2	no	—
151	C₅×C₂²⋊C₄	—	6	1	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
154	#550	—	3	1	no	—
155	#486	—	3	1	no	—
156	#474	—	3	1	no	—
157	#462	C₅×D₃	1	1	yes	characteristic, complemented
158	#331	—	3	1	no	—
159	Q₈⋊C₈	—	3	1	no	—
160	D₄⋊C₈	—	3	1	no	—
161	C₂²×C₃×C₅	#120	1	1	yes	characteristic
162	C₂×C₅×D₃	—	4	2	no	—
163	C₂×C₅×D₃	—	4	1	no	—
164	C₂×C₅×D₃	—	4	1	no	—
165	C₂×C₅×D₃	—	4	2	no	—
166	C₂×C₅×D₃	—	4	2	no	—
167	C₂×C₅×D₃	—	4	1	no	—
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	2	1	no	—
170	C₃×C₄×C₅	—	4	1	no	—
171	C₃×C₄×C₅	—	8	1	no	—
172	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
173	C₃×C₄×C₅	#135	1	1	yes	characteristic
174	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₃×C₄×C₅	#137	1	1	yes	characteristic
176	C₅×Dic₃	—	4	1	no	—
177	C₂×C₃×Q₈	—	2	1	no	—
178	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
179	#239	—	4	2	no	—
180	#239	—	4	2	no	—
181	C₂×D₁₂	—	2	2	no	—
182	C₂×D₁₂	—	2	1	no	—
183	C₂×D₁₂	—	2	1	no	—
184	C₂×D₁₂	—	2	2	no	—
185	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
186	C₂×D₁₂	C₅×D₄	1	2	yes	—
187	C₂×C₄×D₃	—	2	2	no	—
188	C₂×C₄×D₃	—	2	1	no	—
189	C₃×Q₁₆	—	4	2	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
197	(C₂×D₃)⋊C₄	—	2	2	no	—
198	(C₂×D₃)⋊C₄	—	2	1	no	—
199	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
200	C₂×C₃⋊C₈	—	2	1	no	—
201	C₂×C₃⋊C₈	—	2	1	no	—
202	C₂³×C₅	—	6	1	no	—
203	C₂³×C₅	—	6	2	no	—
204	C₅×Q₈	—	2	1	no	—
205	C₅×Q₈	—	4	1	no	—
206	C₅×Q₈	—	4	1	no	—
207	C₅×Q₈	#213	1	2	yes	—
208	C₅×D₄	—	6	1	no	—
209	C₅×D₄	—	6	1	no	—
210	C₅×D₄	—	12	2	no	—
211	C₅×D₄	—	12	4	no	—
212	C₅×D₄	—	12	1	no	—
213	C₅×D₄	—	12	1	no	—
214	C₅×D₄	—	12	1	no	—
215	C₅×D₄	—	12	1	no	—
216	C₅×D₄	—	24	2	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	6	1	no	—
221	C₂×C₄×C₅	—	12	4	no	—
222	C₂×C₄×C₅	—	12	1	no	—
223	C₂×C₄×C₅	—	12	1	no	—
224	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
227	C₅×C₈	—	4	1	no	—
228	C₅×C₈	—	12	1	no	—
229	C₅×C₈	—	12	1	no	—
230	C₂×#41	—	6	1	no	—
231	C₂×Q₁₆	—	2	1	no	—
232	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
233	#127	—	3	1	no	—
234	#127	—	6	1	no	—
235	#121	—	6	2	no	—
236	#121	—	6	1	no	—
237	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
238	C₄×D₄	—	3	1	no	—
239	C₄×D₄	—	6	1	no	—
240	#107	—	6	1	no	—
241	C₄⋊C₈	—	3	1	no	—
242	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
243	#103	—	2	1	no	—
244	#102	—	6	1	no	—
245	#102	—	6	2	no	—
246	C₄×C₈	—	3	1	no	—
247	C₂×C₃×C₅	#447	1	1	yes	characteristic
248	C₂×C₃×C₅	#452	1	1	yes	characteristic
249	C₂×C₃×C₅	#455	1	1	yes	characteristic
250	C₅×D₃	—	8	1	no	—
251	C₅×D₃	—	8	2	no	—
252	C₂²×D₃	—	2	1	no	—
253	C₂²×D₃	—	2	2	no	—
254	C₃×Q₈	—	2	1	no	—
255	C₃×Q₈	—	4	1	no	—
256	C₃×Q₈	—	4	1	no	—
257	C₃×Q₈	C₅×D₈	1	2	yes	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×Dic₃	—	2	1	no	—
265	D₁₂	—	2	1	no	—
266	D₁₂	—	2	1	no	—
267	D₁₂	—	4	2	no	—
268	D₁₂	—	4	4	no	—
269	D₁₂	—	4	1	no	—
270	D₁₂	—	4	1	no	—
271	D₁₂	—	4	1	no	—
272	D₁₂	—	4	1	no	—
273	D₁₂	—	8	2	no	—
274	C₄×D₃	—	4	4	no	—
275	C₄×D₃	—	4	1	no	—
276	C₄×D₃	—	4	1	no	—
277	C₃×C₈	—	4	1	no	—
278	C₃⋊C₈	—	4	1	no	—
279	C₃⋊C₈	—	4	1	no	—
280	C₂²×C₅	—	12	1	no	—
281	C₂²×C₅	—	12	2	no	—
282	C₂²×C₅	—	12	2	no	—
283	C₂²×C₅	—	12	1	no	—
284	C₂²×C₅	—	12	2	no	—
285	C₂²×C₅	—	12	1	no	—
286	C₂²×C₅	#937	1	1	yes	characteristic
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	4	1	no	—
290	C₄×C₅	—	8	1	no	—
291	C₄×C₅	—	12	1	no	—
292	C₄×C₅	#918	1	1	yes	characteristic
293	C₄×C₅	#919	1	1	yes	characteristic
294	C₄×C₅	C₂×#213	1	1	yes	characteristic
295	C₄×C₅	#949	1	1	yes	characteristic
296	#41	—	12	2	no	—
297	#41	—	12	2	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	C₅×#67	1	1	yes	characteristic
300	C₂×D₄	—	3	1	no	—
301	C₂×D₄	—	3	2	no	—
302	C₂×D₄	—	6	2	no	—
303	C₂×D₄	—	6	2	no	—
304	C₂×D₄	—	6	1	no	—
305	C₂×D₄	—	6	1	no	—
306	C₂²×C₄	—	6	2	no	—
307	C₂²×C₄	—	6	1	no	—
308	Q₁₆	—	4	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	6	1	no	—
311	C₂×C₈	—	6	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	3	1	no	—
316	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
317	C₂²⋊C₄	—	6	2	no	—
318	C₂²⋊C₄	—	6	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
321	C₃×C₅	#1641	1	1	yes	characteristic, complemented, Hall
322	C₂²×C₃	C₅×#120	1	1	yes	characteristic
323	C₂×D₃	—	4	2	no	—
324	C₂×D₃	—	4	1	no	—
325	C₂×D₃	—	4	1	no	—
326	C₂×D₃	—	4	2	no	—
327	C₂×D₃	—	4	2	no	—
328	C₂×D₃	—	4	1	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	4	1	no	—
332	C₃×C₄	—	8	1	no	—
333	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
334	C₃×C₄	C₅×#135	1	1	yes	characteristic
335	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
336	C₃×C₄	C₅×#137	1	1	yes	characteristic
337	Dic₃	—	4	1	no	—
338	C₂×C₅	—	24	1	no	—
339	C₂×C₅	—	24	2	no	—
340	C₂×C₅	#5036	1	1	yes	characteristic
341	C₂×C₅	#5187	1	1	yes	characteristic
342	C₂×C₅	#5202	1	1	yes	characteristic
343	C₂³	—	6	1	no	—
344	C₂³	—	6	2	no	—
345	Q₈	—	2	1	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	Q₈	C₅×#213	1	2	yes	—
349	D₄	—	6	1	no	—
350	D₄	—	6	1	no	—
351	D₄	—	12	2	no	—
352	D₄	—	12	4	no	—
353	D₄	—	12	1	no	—
354	D₄	—	12	1	no	—
355	D₄	—	12	1	no	—
356	D₄	—	12	1	no	—
357	D₄	—	24	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	6	1	no	—
362	C₂×C₄	—	12	4	no	—
363	C₂×C₄	—	12	1	no	—
364	C₂×C₄	—	12	1	no	—
365	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
366	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	12	1	no	—
370	C₈	—	12	1	no	—
371	C₂×C₃	C₅×#447	1	1	yes	characteristic
372	C₂×C₃	C₅×#452	1	1	yes	characteristic
373	C₂×C₃	C₅×#455	1	1	yes	characteristic
374	D₃	—	8	1	no	—
375	D₃	—	8	2	no	—
376	C₅	#71061	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	12	1	no	—
378	C₂²	—	12	2	no	—
379	C₂²	—	12	2	no	—
380	C₂²	—	12	1	no	—
381	C₂²	—	12	2	no	—
382	C₂²	—	12	1	no	—
383	C₂²	C₅×#937	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	8	1	no	—
388	C₄	—	12	1	no	—
389	C₄	C₅×#918	1	1	yes	characteristic
390	C₄	C₅×#919	1	1	yes	characteristic
391	C₄	C₂×C₅×#213	1	1	yes	characteristic
392	C₄	C₅×#949	1	1	yes	characteristic
393	C₃	C₅×#1641	1	1	yes	characteristic, complemented, Sylow
394	C₂	—	24	1	no	—
395	C₂	—	24	2	no	—
396	C₂	C₅×#5036	1	1	yes	characteristic
397	C₂	C₅×#5187	1	1	yes	characteristic
398	C₂	C₅×#5202	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#462	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5577	C₂
hypercenter	C₅×#462	D₃
hypocenter	C₃	C₅×#1641
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#462

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#462	C₂	semidirect
3. C₅×#5088	C₂	semidirect
4. C₅×#5087	C₂	semidirect
5. C₅×#4535	C₂	semidirect
6. C₅×#4485	C₂	semidirect
7. C₅×#4483	C₂	semidirect
26. #71061	C₅	direct (N × H)
30. C₅×#462	D₃	semidirect
60. C₃×#462	C₂×C₅	semidirect
61. #5088	C₂×C₅	semidirect
62. #5087	C₂×C₅	semidirect
63. #4535	C₂×C₅	semidirect
64. #4485	C₂×C₅	semidirect
65. #4483	C₂×C₅	semidirect
157. #462	C₅×D₃	semidirect
321. C₃×C₅	#1641	semidirect
376. C₅	#71061	direct (N × H)
393. C₃	C₅×#1641	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5577	2
C₃×C₅×#462	2
C₅×#5088	2
C₅×#5087	2
C₅×#4535	2
C₅×#4485	2
C₅×#4483	2
C₅×#1641	3
#71061	5

Subgroups — C5×#71061 #14290000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71061 #14290000