Subgroups — C₅×#70499 #14282514

Order 1920.

432 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×#5479	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4484	C₂	1	2	yes	maximal, complemented
5	C₅×#4483	C₂	1	2	yes	maximal, complemented
6	C₅×#1495	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×M₁₆	—	2	1	no	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₅×#930	C₄	1	1	yes	characteristic
10	C₅×#929	—	2	1	no	—
11	C₄×C₅×#67	—	2	1	no	—
12	C₅×#924	C₄	1	1	yes	characteristic
13	C₅×#876	—	2	1	no	—
14	C₅×#875	C₄	1	1	yes	characteristic
15	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₅×#872	—	2	1	no	—
17	C₅×#870	C₄	1	1	yes	characteristic
18	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	—	2	1	no	—
20	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₅×#830	—	2	1	no	—
22	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	#70499	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#529	—	3	1	no	—
26	C₅×#431	—	3	1	no	—
27	C₅×#423	D₃	1	1	yes	characteristic, complemented
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×#67	—	2	1	no	—
34	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×C₅×D₃	—	2	1	no	—
36	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
37	C₃×C₅×M₁₆	—	4	2	no	—
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₅×#217	—	2	1	no	—
44	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
45	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
46	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
47	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
48	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₅×Dic₃⋊C₄	—	2	1	no	—
51	C₅×Dic₃⋊C₄	—	2	1	no	—
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	#5479	C₂×C₅	1	1	yes	characteristic
57	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
58	#4925	C₂×C₅	1	1	yes	characteristic, complemented
59	#4484	C₂×C₅	1	2	yes	complemented
60	#4483	C₂×C₅	1	2	yes	complemented
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₅×#126	—	6	1	no	—
63	C₅×#125	—	3	1	no	—
64	C₅×#124	—	3	1	no	—
65	C₅×#123	—	6	1	no	—
66	C₅×C₂²⋊Q₈	—	3	1	no	—
67	C₅×#121	—	3	1	no	—
68	C₄×C₅×Q₈	—	3	1	no	—
69	C₄×C₅×D₄	—	3	1	no	—
70	C₄×C₅×D₄	—	6	1	no	—
71	C₅×#117	—	6	1	no	—
72	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	2	1	no	—
74	C₅×C₄⋊C₈	—	6	1	no	—
75	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
76	C₅×C₂²⋊C₈	—	6	1	no	—
77	C₄×C₅×C₈	—	3	2	no	—
78	#1495	—	3	1	no	Sylow
79	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₅×#67	—	4	2	no	—
92	C₂×C₅×Dic₃	—	2	1	no	—
93	C₂×C₅×Dic₃	—	2	1	no	—
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₅×D₁₂	—	2	2	no	—
96	C₄×C₅×D₃	—	4	1	no	—
97	C₄×C₅×D₃	—	4	1	no	—
98	C₅×Dic₆	—	2	2	no	—
99	C₃×C₅×C₈	—	4	2	no	—
100	C₅×C₃⋊C₈	—	4	2	no	—
101	C₂×C₃×M₁₆	—	2	1	no	—
102	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
103	#930	C₄×C₅	1	1	yes	characteristic
104	#929	—	2	1	no	—
105	C₄×#67	—	2	1	no	—
106	#924	C₄×C₅	1	1	yes	characteristic
107	#876	—	2	1	no	—
108	#875	C₄×C₅	1	1	yes	characteristic
109	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
110	#872	—	2	1	no	—
111	#870	C₄×C₅	1	1	yes	characteristic
112	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
113	C₃×C₄⋊C₈	—	2	1	no	—
114	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
115	#830	—	2	1	no	—
116	C₄⋊(C₃⋊C₈)	—	2	1	no	—
117	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
118	C₂×C₅×Q₈	—	3	1	no	—
119	C₂×C₅×D₄	—	3	1	no	—
120	C₂×C₅×D₄	—	6	1	no	—
121	C₂²×C₄×C₅	—	6	1	no	—
122	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
123	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
124	C₂²×C₄×C₅	#67	1	1	yes	characteristic
125	C₅×M₁₆	—	4	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	6	2	no	—
128	C₅×C₄⋊C₄	—	3	1	no	—
129	C₅×C₄⋊C₄	—	3	1	no	—
130	C₅×C₄⋊C₄	—	6	1	no	—
131	C₅×C₄⋊C₄	—	6	1	no	—
132	C₅×C₄⋊C₄	—	6	1	no	—
133	C₅×C₄⋊C₄	—	6	1	no	—
134	C₅×C₂²⋊C₄	—	6	1	no	—
135	C₅×C₂²⋊C₄	—	6	1	no	—
136	C₅×C₂²⋊C₄	—	6	1	no	—
137	C₅×C₂²⋊C₄	—	6	1	no	—
138	C₅×C₂²⋊C₄	—	6	1	no	—
139	C₄²×C₅	—	6	1	no	—
140	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
141	C₄²×C₅	D₁₂	1	1	yes	characteristic
142	C₄²×C₅	#67	1	1	yes	characteristic
143	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
144	#529	—	3	1	no	—
145	#431	—	3	1	no	—
146	#423	C₅×D₃	1	1	yes	characteristic, complemented
147	Q₈⋊C₈	—	3	2	no	—
148	D₄⋊C₈	—	3	2	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₅×D₃	—	4	1	no	—
154	C₂×C₅×D₃	—	4	1	no	—
155	C₂×C₅×D₃	—	4	1	no	—
156	C₃×C₄×C₅	—	2	1	no	—
157	C₃×C₄×C₅	—	2	1	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	#131	1	2	yes	—
161	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₃×C₄×C₅	#137	1	1	yes	characteristic
163	C₅×Dic₃	—	4	1	no	—
164	C₅×Dic₃	—	4	1	no	—
165	C₅×Dic₃	—	4	1	no	—
166	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
169	C₂×#67	—	2	1	no	—
170	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂×C₄×D₃	—	2	1	no	—
172	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
173	C₃×M₁₆	—	4	2	no	—
174	C₂×C₃×C₈	—	2	2	no	—
175	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
176	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
177	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
178	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
179	#217	—	2	1	no	—
180	(C₂×D₃)⋊C₄	—	2	1	no	—
181	(C₂×D₃)⋊C₄	—	2	1	no	—
182	(C₂×D₃)⋊C₄	—	2	1	no	—
183	(C₂×D₃)⋊C₄	—	2	1	no	—
184	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
185	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
186	Dic₃⋊C₄	—	2	1	no	—
187	Dic₃⋊C₄	—	2	1	no	—
188	Dic₃⋊C₄	—	2	1	no	—
189	Dic₃⋊C₄	—	2	1	no	—
190	C₄×Dic₃	—	2	1	no	—
191	C₂×C₃⋊C₈	—	2	2	no	—
192	C₂³×C₅	—	6	1	no	—
193	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
194	C₅×Q₈	—	6	2	no	—
195	C₅×D₄	—	6	2	no	—
196	C₅×D₄	—	12	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	6	1	no	—
202	C₂×C₄×C₅	—	6	1	no	—
203	C₂×C₄×C₅	—	6	1	no	—
204	C₂×C₄×C₅	—	12	1	no	—
205	C₂×C₄×C₅	—	12	1	no	—
206	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
212	C₅×C₈	—	4	2	no	—
213	C₅×C₈	—	12	2	no	—
214	C₂×M₁₆	—	2	1	no	—
215	#126	—	6	1	no	—
216	#125	—	3	1	no	—
217	#124	—	3	1	no	—
218	#123	—	6	1	no	—
219	C₂²⋊Q₈	—	3	1	no	—
220	#121	—	3	1	no	—
221	C₄×Q₈	—	3	1	no	—
222	C₄×D₄	—	3	1	no	—
223	C₄×D₄	—	6	1	no	—
224	#117	—	6	1	no	—
225	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
226	C₄⋊C₈	—	2	1	no	—
227	C₄⋊C₈	—	6	1	no	—
228	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
229	C₂²⋊C₈	—	6	1	no	—
230	C₄×C₈	—	3	2	no	—
231	C₂×C₃×C₅	—	4	1	no	—
232	C₂×C₃×C₅	#408	1	1	yes	characteristic
233	C₂×C₃×C₅	#417	1	1	yes	characteristic
234	C₂×C₃×C₅	#421	1	1	yes	characteristic
235	C₅×D₃	—	8	1	no	—
236	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×D₃	—	2	1	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	4	1	no	—
242	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	#67	—	4	2	no	—
249	C₂×Dic₃	—	2	1	no	—
250	C₂×Dic₃	—	2	1	no	—
251	C₂×Dic₃	—	2	1	no	—
252	D₁₂	—	2	2	no	—
253	C₄×D₃	—	4	1	no	—
254	C₄×D₃	—	4	1	no	—
255	Dic₆	—	2	2	no	—
256	C₃×C₈	—	4	2	no	—
257	C₃⋊C₈	—	4	2	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	12	1	no	—
262	C₂²×C₅	—	12	1	no	—
263	C₂²×C₅	—	12	1	no	—
264	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	12	1	no	—
270	C₄×C₅	—	12	1	no	—
271	C₄×C₅	—	12	1	no	—
272	C₄×C₅	#907	1	2	yes	—
273	C₄×C₅	#932	1	1	yes	characteristic
274	C₄×C₅	#942	1	1	yes	characteristic
275	C₂×Q₈	—	3	1	no	—
276	C₂×D₄	—	3	1	no	—
277	C₂×D₄	—	6	1	no	—
278	C₂²×C₄	—	6	1	no	—
279	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
280	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
281	C₂²×C₄	C₅×#67	1	1	yes	characteristic
282	M₁₆	—	4	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	6	2	no	—
285	C₄⋊C₄	—	3	1	no	—
286	C₄⋊C₄	—	3	1	no	—
287	C₄⋊C₄	—	6	1	no	—
288	C₄⋊C₄	—	6	1	no	—
289	C₄⋊C₄	—	6	1	no	—
290	C₄⋊C₄	—	6	1	no	—
291	C₂²⋊C₄	—	6	1	no	—
292	C₂²⋊C₄	—	6	1	no	—
293	C₂²⋊C₄	—	6	1	no	—
294	C₂²⋊C₄	—	6	1	no	—
295	C₂²⋊C₄	—	6	1	no	—
296	C₄²	—	6	1	no	—
297	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
298	C₄²	C₅×D₁₂	1	1	yes	characteristic
299	C₄²	C₅×#67	1	1	yes	characteristic
300	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
301	C₃×C₅	#1495	1	1	yes	characteristic, complemented, Hall
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×D₃	—	4	1	no	—
307	C₂×D₃	—	4	1	no	—
308	C₂×D₃	—	4	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	C₅×#131	1	2	yes	—
314	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₃×C₄	C₅×#137	1	1	yes	characteristic
316	Dic₃	—	4	1	no	—
317	Dic₃	—	4	1	no	—
318	Dic₃	—	4	1	no	—
319	C₂×C₅	—	4	1	no	—
320	C₂×C₅	—	24	1	no	—
321	C₂×C₅	#4966	1	1	yes	characteristic
322	C₂×C₅	#5129	1	1	yes	characteristic
323	C₂×C₅	#5139	1	1	yes	characteristic
324	C₂³	—	6	1	no	—
325	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
326	Q₈	—	6	2	no	—
327	D₄	—	6	2	no	—
328	D₄	—	12	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	6	1	no	—
334	C₂×C₄	—	6	1	no	—
335	C₂×C₄	—	6	1	no	—
336	C₂×C₄	—	12	1	no	—
337	C₂×C₄	—	12	1	no	—
338	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
343	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
344	C₈	—	4	2	no	—
345	C₈	—	12	2	no	—
346	C₂×C₃	—	4	1	no	—
347	C₂×C₃	C₅×#408	1	1	yes	characteristic
348	C₂×C₃	C₅×#417	1	1	yes	characteristic
349	C₂×C₃	C₅×#421	1	1	yes	characteristic
350	D₃	—	8	1	no	—
351	C₅	#70499	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	12	1	no	—
356	C₂²	—	12	1	no	—
357	C₂²	—	12	1	no	—
358	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	12	1	no	—
364	C₄	—	12	1	no	—
365	C₄	—	12	1	no	—
366	C₄	C₅×#907	1	2	yes	—
367	C₄	C₅×#932	1	1	yes	characteristic
368	C₄	C₅×#942	1	1	yes	characteristic
369	C₃	C₅×#1495	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	4	1	no	—
371	C₂	—	24	1	no	—
372	C₂	C₅×#4966	1	1	yes	characteristic
373	C₂	C₅×#5129	1	1	yes	characteristic
374	C₂	C₅×#5139	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#423	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#930	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#423	D₃
hypocenter	C₃	C₅×#1495
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#423

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#423	C₂	semidirect
3. C₅×#4925	C₂	semidirect
4. C₅×#4484	C₂	semidirect
5. C₅×#4483	C₂	semidirect
24. #70499	C₅	direct (N × H)
27. C₅×#423	D₃	semidirect
57. C₃×#423	C₂×C₅	semidirect
58. #4925	C₂×C₅	semidirect
59. #4484	C₂×C₅	semidirect
60. #4483	C₂×C₅	semidirect
146. #423	C₅×D₃	semidirect
301. C₃×C₅	#1495	semidirect
351. C₅	#70499	direct (N × H)
369. C₃	C₅×#1495	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5479	2
C₃×C₅×#423	2
C₅×#4925	2
C₅×#4484	2
C₅×#4483	2
C₅×#1495	3
#70499	5

Subgroups — C5×#70499 #14282514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70499 #14282514