Subgroups — C₅×#71923 #14288953

Order 1920.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5027	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5015	C₂	1	1	yes	maximal, characteristic
5	C₅×#4546	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1622	—	3	1	no	maximal, Hall
9	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₃×C₅×#125	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
12	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
17	C₂×C₅×#215	—	2	1	no	—
18	C₂×C₅×#215	—	2	2	no	—
19	C₂×C₅×#213	—	2	1	no	—
20	C₅×#874	C₂²	1	1	yes	characteristic
21	C₅×#809	—	2	1	no	—
22	C₅×#809	—	2	1	no	—
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	#71923	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#554	D₃	1	1	yes	characteristic, complemented
28	C₅×#492	—	3	1	no	—
29	C₅×#460	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#333	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
35	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
36	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×#215	—	4	4	no	—
54	C₅×#215	—	4	2	no	—
55	C₅×#213	—	4	2	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
60	#5085	C₂×C₅	1	1	yes	characteristic, complemented
61	#5027	C₂×C₅	1	1	yes	characteristic, complemented
62	#5015	C₂×C₅	1	1	yes	characteristic
63	#4546	C₂×C₅	1	1	yes	characteristic, complemented
64	#4535	C₂×C₅	1	1	yes	characteristic, complemented
65	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×SD₁₆	—	6	1	no	—
67	C₂×C₅×SD₁₆	—	6	2	no	—
68	C₂×C₅×D₈	—	6	1	no	—
69	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
70	C₅×#127	—	3	1	no	—
71	C₅×#125	—	2	1	no	—
72	C₅×C₂²⋊Q₈	—	2	1	no	—
73	C₅×C₂²⋊Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	—	3	1	no	—
80	C₅×#102	—	6	1	no	—
81	C₅×#102	—	6	1	no	—
82	C₄×C₅×C₈	—	3	1	no	—
83	#1622	—	3	1	no	Sylow
84	C₂³×C₃×C₅	—	2	1	no	—
85	C₂²×C₅×D₃	—	4	1	no	—
86	C₃×C₅×Q₈	—	2	1	no	—
87	C₃×C₅×Q₈	—	2	1	no	—
88	C₃×C₅×Q₈	—	4	2	no	—
89	C₃×C₅×D₄	—	2	1	no	—
90	C₃×C₅×D₄	SD₁₆	1	2	yes	complemented
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	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	8	2	no	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₅×D₁₂	—	4	2	no	—
102	C₅×D₁₂	—	4	1	no	—
103	C₅×D₁₂	—	4	1	no	—
104	C₅×D₁₂	—	4	1	no	—
105	C₅×D₁₂	—	4	1	no	—
106	C₅×C₃⋊C₈	—	2	2	no	—
107	C₅×C₃⋊C₈	—	4	1	no	—
108	C₅×C₃⋊C₈	—	4	1	no	—
109	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
110	C₃×#125	—	2	1	no	—
111	C₃×C₂²⋊Q₈	—	2	1	no	—
112	C₃×C₂²⋊Q₈	—	2	2	no	—
113	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
114	C₃×C₄×D₄	—	2	1	no	—
115	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	—	2	1	no	—
117	C₂×#215	—	2	1	no	—
118	C₂×#215	—	2	2	no	—
119	C₂×#213	—	2	1	no	—
120	#874	C₂²×C₅	1	1	yes	characteristic
121	#809	—	2	1	no	—
122	#809	—	2	1	no	—
123	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
124	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
125	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₅×Q₈	#67	1	1	yes	characteristic
127	C₂×C₅×Q₈	#67	1	2	yes	—
128	C₂×C₅×D₄	—	6	1	no	—
129	C₂×C₅×D₄	—	6	1	no	—
130	C₂×C₅×D₄	—	6	1	no	—
131	C₂×C₅×D₄	#67	1	1	yes	characteristic
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₅×SD₁₆	—	12	4	no	—
135	C₅×SD₁₆	—	12	2	no	—
136	C₅×D₈	—	12	2	no	—
137	C₂×C₅×C₈	—	6	1	no	—
138	C₂×C₅×C₈	—	6	1	no	—
139	C₂×C₅×C₈	—	6	1	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
146	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
147	C₅×C₂²⋊C₄	—	2	2	no	—
148	C₅×C₂²⋊C₄	—	2	1	no	—
149	C₄²×C₅	—	2	1	no	—
150	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
151	#554	C₅×D₃	1	1	yes	characteristic, complemented
152	#492	—	3	1	no	—
153	#460	—	3	1	no	—
154	#459	—	3	1	no	—
155	#333	—	3	1	no	—
156	Q₈⋊C₈	—	3	1	no	—
157	D₄⋊C₈	—	3	1	no	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	4	1	no	—
160	C₂²×C₃×C₅	—	4	1	no	—
161	C₂²×C₃×C₅	#120	1	1	yes	characteristic
162	C₂×C₅×D₃	—	8	1	no	—
163	C₂×C₅×D₃	—	8	1	no	—
164	C₂×C₅×D₃	—	8	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	—	4	1	no	—
168	C₃×C₄×C₅	—	4	1	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
171	C₃×C₄×C₅	#135	1	1	yes	characteristic
172	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₃×C₄×C₅	#137	1	1	yes	characteristic
174	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
175	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
176	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂×D₁₂	—	2	1	no	—
180	C₂×D₁₂	—	2	1	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₄⋊C₄	—	2	2	no	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	2	1	no	—
191	C₃×C₄²	—	2	1	no	—
192	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
193	#215	—	4	4	no	—
194	#215	—	4	2	no	—
195	#213	—	4	2	no	—
196	C₂×C₃⋊C₈	—	2	1	no	—
197	C₂×C₃⋊C₈	—	2	1	no	—
198	C₂×C₃⋊C₈	—	2	1	no	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	12	1	no	—
201	C₅×Q₈	—	2	1	no	—
202	C₅×Q₈	—	2	1	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×D₄	—	2	1	no	—
205	C₅×D₄	—	12	2	no	—
206	C₅×D₄	—	12	1	no	—
207	C₅×D₄	—	12	1	no	—
208	C₅×D₄	—	12	1	no	—
209	C₅×D₄	—	12	1	no	—
210	C₅×D₄	#215	1	2	yes	complemented
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	8	2	no	—
218	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₅×C₈	—	6	2	no	—
222	C₅×C₈	—	12	1	no	—
223	C₅×C₈	—	12	1	no	—
224	C₂×SD₁₆	—	6	1	no	—
225	C₂×SD₁₆	—	6	2	no	—
226	C₂×D₈	—	6	1	no	—
227	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
228	#127	—	3	1	no	—
229	#125	—	2	1	no	—
230	C₂²⋊Q₈	—	2	1	no	—
231	C₂²⋊Q₈	—	2	2	no	—
232	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₄⋊C₈	—	3	1	no	—
237	C₄⋊C₈	—	3	1	no	—
238	#102	—	6	1	no	—
239	#102	—	6	1	no	—
240	C₄×C₈	—	3	1	no	—
241	C₂×C₃×C₅	—	4	2	no	—
242	C₂×C₃×C₅	#448	1	1	yes	characteristic
243	C₂×C₃×C₅	#449	1	1	yes	characteristic
244	C₂×C₃×C₅	#453	1	1	yes	characteristic
245	C₅×D₃	—	16	1	no	—
246	C₂³×C₃	—	2	1	no	—
247	C₂²×D₃	—	4	1	no	—
248	C₃×Q₈	—	2	1	no	—
249	C₃×Q₈	—	2	1	no	—
250	C₃×Q₈	—	4	2	no	—
251	C₃×D₄	—	2	1	no	—
252	C₃×D₄	C₅×SD₁₆	1	2	yes	complemented
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	—	8	2	no	—
260	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	D₁₂	—	4	2	no	—
264	D₁₂	—	4	1	no	—
265	D₁₂	—	4	1	no	—
266	D₁₂	—	4	1	no	—
267	D₁₂	—	4	1	no	—
268	C₃⋊C₈	—	2	2	no	—
269	C₃⋊C₈	—	4	1	no	—
270	C₃⋊C₈	—	4	1	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	—	24	1	no	—
275	C₂²×C₅	—	24	1	no	—
276	C₂²×C₅	—	24	1	no	—
277	C₂²×C₅	#953	1	1	yes	characteristic
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	4	1	no	—
280	C₄×C₅	—	4	1	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	C₂×#215	1	1	yes	characteristic
284	C₄×C₅	#942	1	1	yes	characteristic
285	C₄×C₅	#949	1	1	yes	characteristic
286	C₄×C₅	#950	1	1	yes	characteristic
287	C₂×Q₈	C₅×#67	1	1	yes	characteristic
288	C₂×Q₈	C₅×#67	1	2	yes	—
289	C₂×D₄	—	6	1	no	—
290	C₂×D₄	—	6	1	no	—
291	C₂×D₄	—	6	1	no	—
292	C₂×D₄	C₅×#67	1	1	yes	characteristic
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	SD₁₆	—	12	4	no	—
296	SD₁₆	—	12	2	no	—
297	D₈	—	12	2	no	—
298	C₂×C₈	—	6	1	no	—
299	C₂×C₈	—	6	1	no	—
300	C₂×C₈	—	6	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
307	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
312	C₃×C₅	#1622	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	4	1	no	—
315	C₂²×C₃	—	4	1	no	—
316	C₂²×C₃	C₅×#120	1	1	yes	characteristic
317	C₂×D₃	—	8	1	no	—
318	C₂×D₃	—	8	1	no	—
319	C₂×D₃	—	8	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	—	4	1	no	—
323	C₃×C₄	—	4	1	no	—
324	C₃×C₄	—	4	2	no	—
325	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
326	C₃×C₄	C₅×#135	1	1	yes	characteristic
327	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
328	C₃×C₄	C₅×#137	1	1	yes	characteristic
329	C₂×C₅	—	4	2	no	—
330	C₂×C₅	—	48	1	no	—
331	C₂×C₅	#5227	1	1	yes	characteristic
332	C₂×C₅	#5238	1	1	yes	characteristic
333	C₂×C₅	#5241	1	1	yes	characteristic
334	C₂³	—	2	1	no	—
335	C₂³	—	12	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	4	2	no	—
339	D₄	—	2	1	no	—
340	D₄	—	12	2	no	—
341	D₄	—	12	1	no	—
342	D₄	—	12	1	no	—
343	D₄	—	12	1	no	—
344	D₄	—	12	1	no	—
345	D₄	C₅×#215	1	2	yes	complemented
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
356	C₈	—	6	2	no	—
357	C₈	—	12	1	no	—
358	C₈	—	12	1	no	—
359	C₂×C₃	—	4	2	no	—
360	C₂×C₃	C₅×#448	1	1	yes	characteristic
361	C₂×C₃	C₅×#449	1	1	yes	characteristic
362	C₂×C₃	C₅×#453	1	1	yes	characteristic
363	D₃	—	16	1	no	—
364	C₅	#71923	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	2	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	24	1	no	—
369	C₂²	—	24	1	no	—
370	C₂²	—	24	1	no	—
371	C₂²	C₅×#953	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	C₂×C₅×#215	1	1	yes	characteristic
378	C₄	C₅×#942	1	1	yes	characteristic
379	C₄	C₅×#949	1	1	yes	characteristic
380	C₄	C₅×#950	1	1	yes	characteristic
381	C₃	C₅×#1622	1	1	yes	characteristic, complemented, Sylow
382	C₂	—	4	2	no	—
383	C₂	—	48	1	no	—
384	C₂	C₅×#5227	1	1	yes	characteristic
385	C₂	C₅×#5238	1	1	yes	characteristic
386	C₂	C₅×#5241	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#953
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#554	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5015	C₂
hypercenter	C₅×#554	D₃
hypocenter	C₃	C₅×#1622
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#554

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#554	C₂	semidirect
2. C₅×#5085	C₂	semidirect
3. C₅×#5027	C₂	semidirect
5. C₅×#4546	C₂	semidirect
6. C₅×#4535	C₂	semidirect
7. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
26. #71923	C₅	direct (N × H)
27. C₅×#554	D₃	semidirect
59. C₃×#554	C₂×C₅	semidirect
60. #5085	C₂×C₅	semidirect
61. #5027	C₂×C₅	semidirect
63. #4546	C₂×C₅	semidirect
64. #4535	C₂×C₅	semidirect
65. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
90. C₃×C₅×D₄	SD₁₆	semidirect
151. #554	C₅×D₃	semidirect
210. C₅×D₄	#215	semidirect
252. C₃×D₄	C₅×SD₁₆	semidirect
312. C₃×C₅	#1622	semidirect
345. D₄	C₅×#215	semidirect
364. C₅	#71923	direct (N × H)
381. C₃	C₅×#1622	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#554	2
C₅×#5085	2
C₅×#5027	2
C₅×#5015	2
C₅×#4546	2
C₅×#4535	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1622	3
#71923	5

Subgroups — C5×#71923 #14288953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71923 #14288953