Subgroups — C₅×#71817 #14301378

Order 1920.

664 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×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₅×#5819	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5236	C₂	1	2	yes	maximal, complemented
5	C₅×#4523	C₂	1	2	yes	maximal, complemented
6	C₅×#1884	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
9	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
10	C₃×C₅×#127	C₄	1	1	yes	characteristic, complemented
11	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
12	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
13	C₃×C₅×#121	—	2	2	no	—
14	C₃×C₄×C₅×D₄	—	2	2	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#948	—	2	4	no	—
17	C₅×#926	C₂²	1	2	yes	—
18	C₂×C₅×#208	—	2	2	no	—
19	C₂×C₅×#208	C₂²	1	2	yes	—
20	C₅×#837	—	2	4	no	—
21	C₅×#834	—	2	2	no	—
22	#71817	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅×#568	—	3	1	no	—
24	C₅×#532	D₃	1	1	yes	characteristic
25	C₅×#421	—	3	2	no	—
26	C₅×#410	—	3	1	no	—
27	C₅×#339	—	3	2	no	—
28	C₃×C₅×#41	—	2	2	no	—
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	—	2	2	no	—
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₅×#217	—	2	2	no	—
50	C₅×C₄⋊Dic₃	—	2	2	no	—
51	C₄×C₅×Dic₃	—	2	2	no	—
52	C₅×#208	—	2	4	no	—
53	C₅×#208	—	2	2	no	—
54	C₅×#208	D₄	1	4	yes	complemented
55	C₂×C₅×C₃⋊C₈	—	2	4	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₃×#532	C₂×C₅	1	1	yes	characteristic
58	#5819	C₂×C₅	1	1	yes	characteristic, complemented
59	#5240	C₂×C₅	1	1	yes	characteristic, complemented
60	#5236	C₂×C₅	1	2	yes	complemented
61	#4523	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
63	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
64	C₅×#131	—	6	4	no	—
65	C₂×C₅×M₁₆	—	3	2	no	—
66	C₂×C₅×M₁₆	—	6	2	no	—
67	C₅×C₄⋊Q₈	Dic₃	1	1	yes	characteristic, complemented
68	C₅×#127	Dic₃	1	1	yes	characteristic, complemented
69	C₅×#124	Dic₃	1	1	yes	characteristic, complemented
70	C₅×#124	Dic₃	1	1	yes	characteristic, complemented
71	C₅×#121	—	2	2	no	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₅×#117	—	3	2	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×#104	—	6	4	no	—
76	C₅×#99	—	6	2	no	—
77	#1884	—	3	1	no	Sylow
78	C₂³×C₃×C₅	—	2	1	no	—
79	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	2	2	no	—
82	C₃×C₅×Q₈	—	2	2	no	—
83	C₃×C₅×D₄	—	2	4	no	—
84	C₃×C₅×D₄	—	2	2	no	—
85	C₃×C₅×D₄	—	2	2	no	—
86	C₃×C₅×D₄	—	4	4	no	—
87	C₃×C₅×D₄	—	4	2	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	—	4	1	no	—
95	C₂×C₃×C₄×C₅	—	4	1	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	2	yes	—
101	C₂×C₅×Dic₃	—	4	2	no	—
102	C₅×C₃⋊C₈	—	2	4	no	—
103	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
105	C₃×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic, complemented
106	C₃×#127	C₄×C₅	1	1	yes	characteristic, complemented
107	C₃×#124	C₄×C₅	1	1	yes	characteristic, complemented
108	C₃×#124	C₄×C₅	1	1	yes	characteristic, complemented
109	C₃×#121	—	2	2	no	—
110	C₃×C₄×D₄	—	2	2	no	—
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	#948	—	2	4	no	—
113	#926	C₂²×C₅	1	2	yes	—
114	C₂×#208	—	2	2	no	—
115	C₂×#208	C₂²×C₅	1	2	yes	—
116	#837	—	2	4	no	—
117	#834	—	2	2	no	—
118	C₅×#41	—	2	2	no	—
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	2	2	no	—
121	C₅×#41	—	2	2	no	—
122	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
123	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
128	C₂×C₅×D₄	#67	1	2	yes	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	#67	1	2	yes	—
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₅×M₁₆	—	3	4	no	—
134	C₅×M₁₆	—	6	4	no	—
135	C₅×M₁₆	—	6	2	no	—
136	C₂×C₅×C₈	—	6	4	no	—
137	C₂×C₅×C₈	—	6	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	6	2	no	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	6	2	no	—
143	C₄²×C₅	—	2	1	no	—
144	C₄²×C₅	—	6	2	no	—
145	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
146	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
147	#568	—	3	1	no	—
148	#532	C₅×D₃	1	1	yes	characteristic
149	#421	—	3	2	no	—
150	#410	—	3	1	no	—
151	#339	—	3	2	no	—
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	4	1	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	4	1	no	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	#121	1	2	yes	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	—	2	2	no	—
161	C₃×C₄×C₅	—	4	1	no	—
162	C₃×C₄×C₅	—	4	1	no	—
163	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
164	C₃×C₄×C₅	#120	1	1	yes	characteristic
165	C₃×C₄×C₅	#123	1	1	yes	characteristic
166	C₅×Dic₃	—	8	2	no	—
167	C₃×#41	—	2	2	no	—
168	C₃×#41	—	2	2	no	—
169	C₃×#41	—	2	2	no	—
170	C₃×#41	—	2	2	no	—
171	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₂²⋊C₄	—	2	2	no	—
184	C₃×C₂²⋊C₄	—	2	2	no	—
185	C₃×C₄²	—	2	1	no	—
186	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
187	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
188	#217	—	2	2	no	—
189	C₄⋊Dic₃	—	2	2	no	—
190	C₄×Dic₃	—	2	2	no	—
191	#208	—	2	4	no	—
192	#208	—	2	2	no	—
193	#208	C₅×D₄	1	4	yes	complemented
194	C₂×C₃⋊C₈	—	2	4	no	—
195	C₂×C₃⋊C₈	—	2	2	no	—
196	C₂³×C₅	—	2	1	no	—
197	C₂³×C₅	#217	1	2	yes	—
198	C₂³×C₅	C₂×#67	1	1	yes	characteristic
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	2	2	no	—
201	C₅×D₄	—	2	4	no	—
202	C₅×D₄	—	2	2	no	—
203	C₅×D₄	—	2	2	no	—
204	C₅×D₄	—	4	4	no	—
205	C₅×D₄	—	4	2	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	#217	1	2	yes	—
216	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	#237	1	2	yes	—
218	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
220	C₅×C₈	—	6	4	no	—
221	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
222	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
223	#131	—	6	4	no	—
224	C₂×M₁₆	—	3	2	no	—
225	C₂×M₁₆	—	6	2	no	—
226	C₄⋊Q₈	C₅×Dic₃	1	1	yes	characteristic, complemented
227	#127	C₅×Dic₃	1	1	yes	characteristic, complemented
228	#124	C₅×Dic₃	1	1	yes	characteristic, complemented
229	#124	C₅×Dic₃	1	1	yes	characteristic, complemented
230	#121	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	#117	—	3	2	no	—
233	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
234	#104	—	6	4	no	—
235	#99	—	6	2	no	—
236	C₂×C₃×C₅	—	2	2	no	—
237	C₂×C₃×C₅	—	2	1	no	—
238	C₂×C₃×C₅	—	4	2	no	—
239	C₂×C₃×C₅	—	8	1	no	—
240	C₂×C₃×C₅	#386	1	1	yes	characteristic
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
243	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
244	C₃×Q₈	—	2	2	no	—
245	C₃×Q₈	—	2	2	no	—
246	C₃×D₄	—	2	4	no	—
247	C₃×D₄	—	2	2	no	—
248	C₃×D₄	—	2	2	no	—
249	C₃×D₄	—	4	4	no	—
250	C₃×D₄	—	4	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	4	2	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
260	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₅×#41	1	2	yes	—
264	C₂×Dic₃	—	4	2	no	—
265	C₃⋊C₈	—	2	4	no	—
266	C₂²×C₅	—	2	2	no	—
267	C₂²×C₅	—	4	1	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	1	no	—
271	C₂²×C₅	#939	1	2	yes	—
272	C₂²×C₅	C₂×#217	1	1	yes	characteristic
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	2	no	—
275	C₄×C₅	—	4	1	no	—
276	C₄×C₅	—	4	1	no	—
277	C₄×C₅	—	24	2	no	—
278	C₄×C₅	D₄×Dic₃	1	2	yes	—
279	C₄×C₅	#935	1	1	yes	characteristic
280	C₄×C₅	#937	1	1	yes	characteristic
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
286	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
290	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
291	C₂×D₄	C₅×#67	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	C₅×#67	1	2	yes	—
295	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
296	M₁₆	—	3	4	no	—
297	M₁₆	—	6	4	no	—
298	M₁₆	—	6	2	no	—
299	C₂×C₈	—	6	4	no	—
300	C₂×C₈	—	6	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	6	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	6	2	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	6	2	no	—
308	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
309	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
310	C₃×C₅	#1884	1	1	yes	characteristic, complemented, Hall
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	4	1	no	—
313	C₂²×C₃	—	4	2	no	—
314	C₂²×C₃	—	4	2	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₃	C₅×#121	1	2	yes	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	1	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
323	C₃×C₄	C₅×#120	1	1	yes	characteristic
324	C₃×C₄	C₅×#123	1	1	yes	characteristic
325	Dic₃	—	8	2	no	—
326	C₂×C₅	—	2	1	no	—
327	C₂×C₅	—	2	2	no	—
328	C₂×C₅	—	4	2	no	—
329	C₂×C₅	—	8	1	no	—
330	C₂×C₅	#5220	1	1	yes	characteristic
331	C₂³	—	2	1	no	—
332	C₂³	C₅×#217	1	2	yes	—
333	C₂³	C₂×C₅×#67	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	2	2	no	—
336	D₄	—	2	4	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	12	2	no	—
350	C₂×C₄	C₅×#217	1	2	yes	—
351	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
352	C₂×C₄	C₅×#237	1	2	yes	—
353	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
355	C₈	—	6	4	no	—
356	C₂×C₃	—	2	2	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	4	2	no	—
359	C₂×C₃	—	8	1	no	—
360	C₂×C₃	C₅×#386	1	1	yes	characteristic
361	C₅	#71817	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²	—	2	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	C₅×#939	1	2	yes	—
368	C₂²	C₂×C₅×#217	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	24	2	no	—
374	C₄	C₅×D₄×Dic₃	1	2	yes	—
375	C₄	C₅×#935	1	1	yes	characteristic
376	C₄	C₅×#937	1	1	yes	characteristic
377	C₃	C₅×#1884	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	2	1	no	—
379	C₂	—	2	2	no	—
380	C₂	—	4	2	no	—
381	C₂	—	8	1	no	—
382	C₂	C₅×#5220	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#937
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting, prime radical	C₃×C₅×#532	C₂
socle	C₂×C₃×C₅	#386
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#1884
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#532

Complements

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

N	H ≅ G/N	type
2. C₅×#5819	C₂	semidirect
3. C₅×#5240	C₂	semidirect
4. C₅×#5236	C₂	semidirect
5. C₅×#4523	C₂	semidirect
9. C₃×C₅×C₄⋊Q₈	C₄	semidirect
10. C₃×C₅×#127	C₄	semidirect
11. C₃×C₅×#124	C₄	semidirect
12. C₃×C₅×#124	C₄	semidirect
22. #71817	C₅	direct (N × H)
54. C₅×#208	D₄	semidirect
58. #5819	C₂×C₅	semidirect
59. #5240	C₂×C₅	semidirect
60. #5236	C₂×C₅	semidirect
61. #4523	C₂×C₅	semidirect
67. C₅×C₄⋊Q₈	Dic₃	semidirect
68. C₅×#127	Dic₃	semidirect
69. C₅×#124	Dic₃	semidirect
70. C₅×#124	Dic₃	semidirect
105. C₃×C₄⋊Q₈	C₄×C₅	semidirect
106. C₃×#127	C₄×C₅	semidirect
107. C₃×#124	C₄×C₅	semidirect
108. C₃×#124	C₄×C₅	semidirect
193. #208	C₅×D₄	semidirect
226. C₄⋊Q₈	C₅×Dic₃	semidirect
227. #127	C₅×Dic₃	semidirect
228. #124	C₅×Dic₃	semidirect
229. #124	C₅×Dic₃	semidirect
310. C₃×C₅	#1884	semidirect
361. C₅	#71817	direct (N × H)
377. C₃	C₅×#1884	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₅×#5819	2
C₅×#5240	2
C₅×#5236	2
C₅×#4523	2
C₅×#1884	3
#71817	5

Subgroups — C5×#71817 #14301378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71817 #14301378