Subgroups — C₅×#72021 #14301375

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×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5832	C₂	1	1	yes	maximal, characteristic
3	C₅×#5240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5139	C₂	1	2	yes	maximal, complemented
5	C₅×#4555	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×C₅×#235	C₂²	1	1	yes	characteristic
9	C₃×C₅×#131	—	2	4	no	—
10	C₂×C₃×C₅×M₁₆	—	2	2	no	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₅×#947	C₄	1	1	yes	characteristic, complemented
13	C₅×#944	C₄	1	1	yes	characteristic, complemented
14	C₅×#940	C₄	1	1	yes	characteristic, complemented
15	C₅×#939	—	2	2	no	—
16	C₅×#936	C₄	1	1	yes	characteristic, complemented
17	C₄×C₅×#67	—	2	2	no	—
18	C₅×#926	C₂²	1	2	yes	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₅×#834	—	2	2	no	—
21	C₅×#825	—	2	4	no	—
22	#72021	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅×#568	D₃	1	1	yes	characteristic, complemented
24	C₅×#532	—	3	1	no	—
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	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×#67	—	2	2	no	—
36	C₂×C₅×#67	—	2	1	no	—
37	C₂²×C₅×Dic₃	—	2	1	no	—
38	C₅×#235	—	2	2	no	—
39	C₅×#235	—	2	2	no	—
40	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×M₁₆	—	2	4	no	—
44	C₃×C₅×M₁₆	—	2	2	no	—
45	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
46	C₂×C₃×C₅×C₈	—	2	4	no	—
47	C₂×C₃×C₅×C₈	—	2	2	no	—
48	C₅×#217	—	2	2	no	—
49	C₅×#217	—	2	2	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₅×C₄⋊Dic₃	—	2	2	no	—
52	C₅×Dic₃⋊C₄	—	2	2	no	—
53	C₄×C₅×Dic₃	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	2	no	—
55	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₃×#568	C₂×C₅	1	1	yes	characteristic, complemented
58	#5832	C₂×C₅	1	1	yes	characteristic
59	#5240	C₂×C₅	1	1	yes	characteristic, complemented
60	#5139	C₂×C₅	1	2	yes	complemented
61	#4555	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×#41	—	3	1	no	—
63	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
64	C₅×#131	—	2	4	no	—
65	C₂×C₅×M₁₆	—	2	2	no	—
66	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
67	C₅×C₄⋊Q₈	—	3	1	no	—
68	C₅×#127	—	3	1	no	—
69	C₅×#124	—	3	1	no	—
70	C₅×#124	—	3	1	no	—
71	C₅×#121	—	6	2	no	—
72	C₄×C₅×D₄	—	6	2	no	—
73	C₅×#117	—	3	2	no	—
74	C₂×C₄²×C₅	—	3	1	no	—
75	C₅×#104	—	6	4	no	—
76	C₅×#99	—	6	2	no	—
77	#1884	—	3	1	no	Sylow
78	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
79	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	2	1	no	—
81	C₃×C₅×Q₈	—	2	2	no	—
82	C₃×C₅×D₄	—	2	4	no	—
83	C₃×C₅×D₄	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	#41	1	2	yes	—
91	C₅×#67	—	4	4	no	—
92	C₅×#67	—	4	2	no	—
93	C₂×C₅×Dic₃	—	2	1	no	—
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₂×C₅×Dic₃	—	4	2	no	—
97	C₂×C₅×Dic₃	—	4	2	no	—
98	C₅×D₁₂	—	2	2	no	—
99	C₄×C₅×D₃	—	4	1	no	—
100	C₄×C₅×D₃	—	4	1	no	—
101	C₅×Dic₆	—	2	2	no	—
102	C₃×C₅×C₈	—	2	4	no	—
103	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
104	C₂×#235	C₂²×C₅	1	1	yes	characteristic
105	C₃×#131	—	2	4	no	—
106	C₂×C₃×M₁₆	—	2	2	no	—
107	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
108	#947	C₄×C₅	1	1	yes	characteristic, complemented
109	#944	C₄×C₅	1	1	yes	characteristic, complemented
110	#940	C₄×C₅	1	1	yes	characteristic, complemented
111	#939	—	2	2	no	—
112	#936	C₄×C₅	1	1	yes	characteristic, complemented
113	C₄×#67	—	2	2	no	—
114	#926	C₂²×C₅	1	2	yes	—
115	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
116	#834	—	2	2	no	—
117	#825	—	2	4	no	—
118	C₅×#41	—	2	2	no	—
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	6	2	no	—
121	C₅×#41	—	6	2	no	—
122	C₂×C₅×Q₈	—	3	1	no	—
123	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
124	C₂×C₅×D₄	—	3	1	no	—
125	C₂×C₅×D₄	—	6	2	no	—
126	C₂×C₅×D₄	—	6	1	no	—
127	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
128	C₂×C₅×D₄	D₁₂	1	2	yes	—
129	C₂²×C₄×C₅	—	6	1	no	—
130	C₂²×C₄×C₅	—	6	1	no	—
131	C₂²×C₄×C₅	#67	1	2	yes	—
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₅×M₁₆	—	2	4	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₅×M₁₆	#67	1	4	yes	complemented
136	C₂×C₅×C₈	—	2	4	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₅×C₄⋊C₄	—	6	2	no	—
139	C₅×C₄⋊C₄	—	6	2	no	—
140	C₅×C₂²⋊C₄	—	6	2	no	—
141	C₅×C₂²⋊C₄	—	6	2	no	—
142	C₅×C₂²⋊C₄	—	6	2	no	—
143	C₄²×C₅	—	3	1	no	—
144	C₄²×C₅	—	3	1	no	—
145	C₄²×C₅	—	6	1	no	—
146	C₄²×C₅	—	6	2	no	—
147	#568	C₅×D₃	1	1	yes	characteristic, complemented
148	#532	—	3	1	no	—
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₃×C₅	#121	1	2	yes	—
157	C₂×C₅×D₃	—	4	2	no	—
158	C₂×C₅×D₃	—	4	1	no	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
161	C₃×C₄×C₅	#120	1	1	yes	characteristic
162	C₃×C₄×C₅	#123	1	1	yes	characteristic
163	C₅×Dic₃	—	2	2	no	—
164	C₅×Dic₃	—	4	1	no	—
165	C₅×Dic₃	—	4	1	no	—
166	C₅×Dic₃	—	8	2	no	—
167	C₃×#41	—	2	2	no	—
168	C₃×#41	—	2	2	no	—
169	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
172	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂×#67	—	2	2	no	—
175	C₂×#67	—	2	1	no	—
176	C₂²×Dic₃	—	2	1	no	—
177	#235	—	2	2	no	—
178	#235	—	2	2	no	—
179	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
180	C₂×C₄×D₃	—	2	1	no	—
181	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
182	C₃×M₁₆	—	2	4	no	—
183	C₃×M₁₆	—	2	2	no	—
184	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
185	C₂×C₃×C₈	—	2	4	no	—
186	C₂×C₃×C₈	—	2	2	no	—
187	#217	—	2	2	no	—
188	#217	—	2	2	no	—
189	(C₂×D₃)⋊C₄	—	2	2	no	—
190	C₄⋊Dic₃	—	2	2	no	—
191	Dic₃⋊C₄	—	2	2	no	—
192	C₄×Dic₃	—	2	1	no	—
193	C₄×Dic₃	—	2	2	no	—
194	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
195	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
196	C₂³×C₅	—	6	1	no	—
197	C₂³×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
198	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	6	2	no	—
201	C₅×D₄	—	2	4	no	—
202	C₅×D₄	—	2	2	no	—
203	C₅×D₄	—	6	2	no	—
204	C₅×D₄	—	12	4	no	—
205	C₅×D₄	—	12	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	6	1	no	—
209	C₂×C₄×C₅	—	6	1	no	—
210	C₂×C₄×C₅	—	6	1	no	—
211	C₂×C₄×C₅	—	12	2	no	—
212	C₂×C₄×C₅	—	12	1	no	—
213	C₂×C₄×C₅	—	12	1	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
216	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
217	C₂×C₄×C₅	#235	1	2	yes	—
218	C₂×C₄×C₅	C₂×#67	1	2	yes	—
219	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
220	C₅×C₈	—	2	4	no	—
221	C₂×#41	—	3	1	no	—
222	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
223	#131	—	2	4	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
226	C₄⋊Q₈	—	3	1	no	—
227	#127	—	3	1	no	—
228	#124	—	3	1	no	—
229	#124	—	3	1	no	—
230	#121	—	6	2	no	—
231	C₄×D₄	—	6	2	no	—
232	#117	—	3	2	no	—
233	C₂×C₄²	—	3	1	no	—
234	#104	—	6	4	no	—
235	#99	—	6	2	no	—
236	C₂×C₃×C₅	—	2	1	no	—
237	C₂×C₃×C₅	—	2	2	no	—
238	C₂×C₃×C₅	—	4	2	no	—
239	C₂×C₃×C₅	#386	1	1	yes	characteristic
240	C₅×D₃	—	8	1	no	—
241	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
242	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
243	C₂²×D₃	—	2	1	no	—
244	C₃×Q₈	—	2	2	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
250	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₅×#41	1	2	yes	—
254	#67	—	4	4	no	—
255	#67	—	4	2	no	—
256	C₂×Dic₃	—	2	1	no	—
257	C₂×Dic₃	—	2	1	no	—
258	C₂×Dic₃	—	2	1	no	—
259	C₂×Dic₃	—	4	2	no	—
260	C₂×Dic₃	—	4	2	no	—
261	D₁₂	—	2	2	no	—
262	C₄×D₃	—	4	1	no	—
263	C₄×D₃	—	4	1	no	—
264	Dic₆	—	2	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	—	12	2	no	—
270	C₂²×C₅	—	12	1	no	—
271	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
272	C₂²×C₅	#930	1	2	yes	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	6	2	no	—
275	C₄×C₅	—	12	1	no	—
276	C₄×C₅	—	12	1	no	—
277	C₄×C₅	—	24	2	no	—
278	C₄×C₅	C₄×#67	1	2	yes	—
279	C₄×C₅	#929	1	1	yes	characteristic
280	C₄×C₅	#953	1	1	yes	characteristic
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	#41	—	6	2	no	—
284	#41	—	6	2	no	—
285	C₂×Q₈	—	3	1	no	—
286	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
287	C₂×D₄	—	3	1	no	—
288	C₂×D₄	—	6	2	no	—
289	C₂×D₄	—	6	1	no	—
290	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
291	C₂×D₄	C₅×D₁₂	1	2	yes	—
292	C₂²×C₄	—	6	1	no	—
293	C₂²×C₄	—	6	1	no	—
294	C₂²×C₄	C₅×#67	1	2	yes	—
295	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
296	M₁₆	—	2	4	no	—
297	M₁₆	—	2	2	no	—
298	M₁₆	C₅×#67	1	4	yes	complemented
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₄⋊C₄	—	6	2	no	—
302	C₄⋊C₄	—	6	2	no	—
303	C₂²⋊C₄	—	6	2	no	—
304	C₂²⋊C₄	—	6	2	no	—
305	C₂²⋊C₄	—	6	2	no	—
306	C₄²	—	3	1	no	—
307	C₄²	—	3	1	no	—
308	C₄²	—	6	1	no	—
309	C₄²	—	6	2	no	—
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	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₃	C₅×#121	1	2	yes	—
316	C₂×D₃	—	4	2	no	—
317	C₂×D₃	—	4	1	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
320	C₃×C₄	C₅×#120	1	1	yes	characteristic
321	C₃×C₄	C₅×#123	1	1	yes	characteristic
322	Dic₃	—	2	2	no	—
323	Dic₃	—	4	1	no	—
324	Dic₃	—	4	1	no	—
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	—	24	1	no	—
330	C₂×C₅	#5213	1	1	yes	characteristic
331	C₂³	—	6	1	no	—
332	C₂³	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
333	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	6	2	no	—
336	D₄	—	2	4	no	—
337	D₄	—	2	2	no	—
338	D₄	—	6	2	no	—
339	D₄	—	12	4	no	—
340	D₄	—	12	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	6	1	no	—
344	C₂×C₄	—	6	1	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	12	2	no	—
347	C₂×C₄	—	12	1	no	—
348	C₂×C₄	—	12	1	no	—
349	C₂×C₄	—	12	2	no	—
350	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
351	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
352	C₂×C₄	C₅×#235	1	2	yes	—
353	C₂×C₄	C₂×C₅×#67	1	2	yes	—
354	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
355	C₈	—	2	4	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	4	2	no	—
359	C₂×C₃	C₅×#386	1	1	yes	characteristic
360	D₃	—	8	1	no	—
361	C₅	#72021	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	—	12	2	no	—
366	C₂²	—	12	1	no	—
367	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
368	C₂²	C₅×#930	1	2	yes	—
369	C₄	—	2	2	no	—
370	C₄	—	6	2	no	—
371	C₄	—	12	1	no	—
372	C₄	—	12	1	no	—
373	C₄	—	24	2	no	—
374	C₄	C₄×C₅×#67	1	2	yes	—
375	C₄	C₅×#929	1	1	yes	characteristic
376	C₄	C₅×#953	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	—	24	1	no	—
382	C₂	C₅×#5213	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#953
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#568	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₅×#5832	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#568	D₃
hypocenter	C₃	C₅×#1884
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#568

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#568	C₂	semidirect
3. C₅×#5240	C₂	semidirect
4. C₅×#5139	C₂	semidirect
5. C₅×#4555	C₂	semidirect
12. C₅×#947	C₄	semidirect
13. C₅×#944	C₄	semidirect
14. C₅×#940	C₄	semidirect
16. C₅×#936	C₄	semidirect
22. #72021	C₅	direct (N × H)
23. C₅×#568	D₃	semidirect
45. C₃×C₅×M₁₆	D₄	semidirect
57. C₃×#568	C₂×C₅	semidirect
59. #5240	C₂×C₅	semidirect
60. #5139	C₂×C₅	semidirect
61. #4555	C₂×C₅	semidirect
108. #947	C₄×C₅	semidirect
109. #944	C₄×C₅	semidirect
110. #940	C₄×C₅	semidirect
112. #936	C₄×C₅	semidirect
135. C₅×M₁₆	#67	semidirect
147. #568	C₅×D₃	semidirect
184. C₃×M₁₆	C₅×D₄	semidirect
298. M₁₆	C₅×#67	semidirect
310. C₃×C₅	#1884	semidirect
361. C₅	#72021	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×#568	2
C₅×#5832	2
C₅×#5240	2
C₅×#5139	2
C₅×#4555	2
C₅×#1884	3
#72021	5

Subgroups — C5×#72021 #14301375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#72021 #14301375