Subgroups — C₅×#71859 #14313260

Order 1920.

532 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	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic
2	C₅×#5240	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4536	C₂	1	4	yes	maximal, complemented
5	C₅×#2122	—	3	1	no	maximal, Hall
6	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic, complemented
8	C₃×C₅×#127	—	2	1	no	—
9	C₃×C₅×#124	—	2	1	no	—
10	C₃×C₅×#121	—	2	1	no	—
11	C₃×C₅×#121	—	2	1	no	—
12	C₃×C₅×#120	C₄	1	2	yes	complemented
13	C₃×C₅×#120	C₂²	1	2	yes	—
14	C₃×C₅×#117	C₄	1	1	yes	characteristic, complemented
15	C₅×#926	—	2	1	no	—
16	C₂×C₅×#208	—	2	1	no	—
17	C₅×#836	—	2	1	no	—
18	C₅×#834	—	2	1	no	—
19	C₅×#834	C₂²	1	2	yes	—
20	C₅×#833	C₂²	1	2	yes	—
21	#71859	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₅×#535	D₃	1	1	yes	characteristic
23	C₅×#413	—	3	1	no	—
24	C₅×#410	—	3	1	no	—
25	C₅×AΣL(1,𝔽₁₆)	—	3	4	no	—
26	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
27	C₃×C₅×#41	—	4	1	no	—
28	C₃×C₅×#41	—	4	1	no	—
29	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	2	1	no	—
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	4	1	no	—
35	C₂×C₃×C₅×D₄	—	4	1	no	—
36	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
38	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
45	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₅×#217	—	2	2	no	—
48	C₅×C₄⋊Dic₃	—	4	1	no	—
49	C₄×C₅×Dic₃	—	4	1	no	—
50	C₅×#208	—	2	2	no	—
51	C₅×#208	—	4	1	no	—
52	C₂×C₅×C₃⋊C₈	—	4	1	no	—
53	C₃×#535	C₂×C₅	1	1	yes	characteristic
54	#5240	C₂×C₅	1	1	yes	characteristic, complemented
55	#5237	C₂×C₅	1	1	yes	characteristic, complemented
56	#4536	C₂×C₅	1	4	yes	complemented
57	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
58	C₂²×C₅×D₄	Dic₃	1	1	yes	characteristic, complemented
59	C₂×C₅×M₁₆	—	6	1	no	—
60	C₅×#127	—	2	1	no	—
61	C₅×#124	—	2	1	no	—
62	C₅×#121	—	2	1	no	—
63	C₅×#121	—	2	1	no	—
64	C₅×#120	Dic₃	1	2	yes	complemented
65	C₅×#120	C₂×D₃	1	2	yes	—
66	C₅×#117	—	6	1	no	—
67	C₅×#117	Dic₃	1	1	yes	characteristic, complemented
68	C₅×#101	—	6	1	no	—
69	C₅×#100	—	3	2	no	—
70	C₅×#99	—	3	2	no	—
71	C₅×#99	—	6	1	no	—
72	#2122	—	3	1	no	Sylow
73	C₂³×C₃×C₅	—	2	2	no	—
74	C₂³×C₃×C₅	—	4	2	no	—
75	C₂³×C₃×C₅	—	8	2	no	—
76	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₃×C₅×Q₈	—	4	1	no	—
80	C₃×C₅×D₄	—	4	1	no	—
81	C₃×C₅×D₄	—	4	1	no	—
82	C₃×C₅×D₄	—	4	1	no	—
83	C₃×C₅×D₄	—	4	2	no	—
84	C₃×C₅×D₄	—	4	1	no	—
85	C₃×C₅×D₄	—	4	1	no	—
86	C₃×C₅×D₄	—	8	2	no	—
87	C₃×C₅×D₄	—	8	2	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₅×Dic₃	—	4	2	no	—
100	C₅×C₃⋊C₈	—	4	2	no	—
101	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃×D₄	C₄×C₅	1	1	yes	characteristic, complemented
103	C₃×#127	—	2	1	no	—
104	C₃×#124	—	2	1	no	—
105	C₃×#121	—	2	1	no	—
106	C₃×#121	—	2	1	no	—
107	C₃×#120	C₄×C₅	1	2	yes	complemented
108	C₃×#120	C₂²×C₅	1	2	yes	—
109	C₃×#117	C₄×C₅	1	1	yes	characteristic, complemented
110	#926	—	2	1	no	—
111	C₂×#208	—	2	1	no	—
112	#836	—	2	1	no	—
113	#834	—	2	1	no	—
114	#834	C₂²×C₅	1	2	yes	—
115	#833	C₂²×C₅	1	2	yes	—
116	C₂⁴×C₅	C₂×Dic₃	1	2	yes	—
117	C₅×#41	—	4	1	no	—
118	C₅×#41	—	4	1	no	—
119	C₂×C₅×Q₈	#67	1	1	yes	characteristic
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	4	1	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
127	C₂×C₅×D₄	#67	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
130	C₂²×C₄×C₅	#67	1	1	yes	characteristic
131	C₂²×C₄×C₅	#67	1	1	yes	characteristic
132	C₅×M₁₆	—	6	2	no	—
133	C₅×M₁₆	—	12	1	no	—
134	C₂×C₅×C₈	—	12	1	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	12	1	no	—
137	C₅×C₂²⋊C₄	—	2	2	no	—
138	C₅×C₂²⋊C₄	—	2	2	no	—
139	C₅×C₂²⋊C₄	—	6	2	no	—
140	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
141	C₄²×C₅	—	2	1	no	—
142	C₄²×C₅	—	12	1	no	—
143	#535	C₅×D₃	1	1	yes	characteristic
144	#413	—	3	1	no	—
145	#410	—	3	1	no	—
146	AΣL(1,𝔽₁₆)	—	3	4	no	—
147	C₂²×C₃×C₅	—	2	1	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	4	1	no	—
151	C₂²×C₃×C₅	—	4	1	no	—
152	C₂²×C₃×C₅	—	4	1	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	8	4	no	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	4	2	no	—
162	C₃×C₄×C₅	#99	1	1	yes	characteristic
163	C₃×C₄×C₅	#99	1	1	yes	characteristic
164	C₅×Dic₃	—	8	2	no	—
165	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
166	C₃×#41	—	4	1	no	—
167	C₃×#41	—	4	1	no	—
168	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	—	2	2	no	—
171	C₂×C₃×D₄	—	2	1	no	—
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	—	4	1	no	—
174	C₂×C₃×D₄	—	4	1	no	—
175	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₂²⋊C₄	—	2	2	no	—
183	C₃×C₂²⋊C₄	—	2	2	no	—
184	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
185	C₃×C₄²	—	2	1	no	—
186	#217	—	2	2	no	—
187	C₄⋊Dic₃	—	4	1	no	—
188	C₄×Dic₃	—	4	1	no	—
189	#208	—	2	2	no	—
190	#208	—	4	1	no	—
191	C₂×C₃⋊C₈	—	4	1	no	—
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	4	2	no	—
194	C₂³×C₅	—	8	2	no	—
195	C₂³×C₅	#217	1	1	yes	characteristic
196	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
197	C₂³×C₅	C₂×#67	1	1	yes	characteristic
198	C₅×Q₈	—	4	1	no	—
199	C₅×D₄	—	4	1	no	—
200	C₅×D₄	—	4	1	no	—
201	C₅×D₄	—	4	1	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	1	no	—
204	C₅×D₄	—	4	1	no	—
205	C₅×D₄	—	8	2	no	—
206	C₅×D₄	—	8	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	#217	1	1	yes	characteristic
216	C₂×C₄×C₅	#217	1	1	yes	characteristic
217	C₂×C₄×C₅	#217	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
219	C₅×C₈	—	12	2	no	—
220	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
221	C₂²×D₄	C₅×Dic₃	1	1	yes	characteristic, complemented
222	C₂×M₁₆	—	6	1	no	—
223	#127	—	2	1	no	—
224	#124	—	2	1	no	—
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#120	C₅×Dic₃	1	2	yes	complemented
228	#120	C₂×C₅×D₃	1	2	yes	—
229	#117	—	6	1	no	—
230	#117	C₅×Dic₃	1	1	yes	characteristic, complemented
231	#101	—	6	1	no	—
232	#100	—	3	2	no	—
233	#99	—	3	2	no	—
234	#99	—	6	1	no	—
235	C₂×C₃×C₅	—	2	1	no	—
236	C₂×C₃×C₅	—	4	1	no	—
237	C₂×C₃×C₅	—	4	1	no	—
238	C₂×C₃×C₅	—	4	1	no	—
239	C₂×C₃×C₅	—	8	2	no	—
240	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
241	C₂³×C₃	—	2	2	no	—
242	C₂³×C₃	—	4	2	no	—
243	C₂³×C₃	—	8	2	no	—
244	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
245	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
246	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
247	C₃×Q₈	—	4	1	no	—
248	C₃×D₄	—	4	1	no	—
249	C₃×D₄	—	4	1	no	—
250	C₃×D₄	—	4	1	no	—
251	C₃×D₄	—	4	2	no	—
252	C₃×D₄	—	4	1	no	—
253	C₃×D₄	—	4	1	no	—
254	C₃×D₄	—	8	2	no	—
255	C₃×D₄	—	8	2	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×Dic₃	—	4	2	no	—
268	C₃⋊C₈	—	4	2	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	—	4	1	no	—
275	C₂²×C₅	—	4	2	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	8	4	no	—
279	C₂²×C₅	C₂×#217	1	1	yes	characteristic
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	2	1	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	24	2	no	—
285	C₄×C₅	#834	1	1	yes	characteristic
286	C₄×C₅	#834	1	1	yes	characteristic
287	C₂⁴	C₂×C₅×Dic₃	1	2	yes	—
288	#41	—	4	1	no	—
289	#41	—	4	1	no	—
290	C₂×Q₈	C₅×#67	1	1	yes	characteristic
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
298	C₂×D₄	C₅×#67	1	1	yes	characteristic
299	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
301	C₂²×C₄	C₅×#67	1	1	yes	characteristic
302	C₂²×C₄	C₅×#67	1	1	yes	characteristic
303	M₁₆	—	6	2	no	—
304	M₁₆	—	12	1	no	—
305	C₂×C₈	—	12	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	12	1	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	6	2	no	—
311	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
312	C₄²	—	2	1	no	—
313	C₄²	—	12	1	no	—
314	C₃×C₅	#2122	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	4	1	no	—
319	C₂²×C₃	—	4	1	no	—
320	C₂²×C₃	—	4	1	no	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	8	4	no	—
325	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	4	2	no	—
330	C₃×C₄	C₅×#99	1	1	yes	characteristic
331	C₃×C₄	C₅×#99	1	1	yes	characteristic
332	Dic₃	—	8	2	no	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	4	1	no	—
335	C₂×C₅	—	4	1	no	—
336	C₂×C₅	—	4	1	no	—
337	C₂×C₅	—	8	2	no	—
338	C₂×C₅	C₂×#834	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	8	2	no	—
342	C₂³	C₅×#217	1	1	yes	characteristic
343	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
344	C₂³	C₂×C₅×#67	1	1	yes	characteristic
345	Q₈	—	4	1	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	12	2	no	—
362	C₂×C₄	C₅×#217	1	1	yes	characteristic
363	C₂×C₄	C₅×#217	1	1	yes	characteristic
364	C₂×C₄	C₅×#217	1	1	yes	characteristic
365	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
366	C₈	—	12	2	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	4	1	no	—
369	C₂×C₃	—	4	1	no	—
370	C₂×C₃	—	4	1	no	—
371	C₂×C₃	—	8	2	no	—
372	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
373	C₅	#71859	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	8	4	no	—
384	C₂²	C₂×C₅×#217	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	24	2	no	—
390	C₄	C₅×#834	1	1	yes	characteristic
391	C₄	C₅×#834	1	1	yes	characteristic
392	C₃	C₅×#2122	1	1	yes	characteristic, complemented, Sylow
393	C₂	—	2	1	no	—
394	C₂	—	4	1	no	—
395	C₂	—	4	1	no	—
396	C₂	—	4	1	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×C₅×#834	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#834
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂×D₄	C₂²×C₅×D₃
Fitting, prime radical	C₃×C₅×#535	C₂
socle	C₂×C₃×C₅	C₂×#99
cosocle	C₂×C₃×D₄	C₂³×C₅
hypercenter	C₅×#535	D₃
hypocenter	C₃	C₅×#2122
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#41 ◁ C₅×#535

Complements

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

N	H ≅ G/N	type
2. C₅×#5240	C₂	semidirect
3. C₅×#5237	C₂	semidirect
4. C₅×#4536	C₂	semidirect
7. C₂²×C₃×C₅×D₄	C₄	semidirect
12. C₃×C₅×#120	C₄	semidirect
14. C₃×C₅×#117	C₄	semidirect
21. #71859	C₅	direct (N × H)
54. #5240	C₂×C₅	semidirect
55. #5237	C₂×C₅	semidirect
56. #4536	C₂×C₅	semidirect
58. C₂²×C₅×D₄	Dic₃	semidirect
64. C₅×#120	Dic₃	semidirect
67. C₅×#117	Dic₃	semidirect
102. C₂²×C₃×D₄	C₄×C₅	semidirect
107. C₃×#120	C₄×C₅	semidirect
109. C₃×#117	C₄×C₅	semidirect
221. C₂²×D₄	C₅×Dic₃	semidirect
227. #120	C₅×Dic₃	semidirect
230. #117	C₅×Dic₃	semidirect
314. C₃×C₅	#2122	semidirect
373. C₅	#71859	direct (N × H)
392. C₃	C₅×#2122	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#535	2
C₅×#5240	2
C₅×#5237	2
C₅×#4536	2
C₅×#2122	3
#71859	5

Subgroups — C5×#71859 #14313260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71859 #14313260