Subgroups — C₅×#83286 #14439078

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 392 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, complemented
2	C₂×C₅×#950	C₂	1	4	yes	maximal, complemented
3	C₅×#5477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5086	C₂	1	2	yes	maximal, complemented
5	C₅×#5074	C₂	1	2	yes	maximal, complemented
6	C₅×#5060	C₂	1	2	yes	maximal, complemented
7	C₅×#5058	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3150	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂×C₅×#235	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×#127	C₂²	1	1	yes	characteristic
14	C₃×C₅×#124	C₂²	1	2	yes	—
15	C₃×C₅×#121	—	2	2	no	—
16	C₃×C₄×C₅×D₄	—	2	2	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#950	—	2	16	no	—
19	C₂×C₅×#216	C₂²	1	4	yes	—
20	C₂×C₅×#215	C₂²	1	4	yes	—
21	C₂×C₅×#214	C₂²	1	4	yes	—
22	C₂×C₅×#213	C₂²	1	4	yes	—
23	C₅×#930	—	2	2	no	—
24	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
25	C₅×#875	C₂²	1	2	yes	—
26	C₅×#874	C₂²	1	1	yes	characteristic
27	C₄×C₅×D₁₂	—	2	2	no	—
28	C₅×#869	C₂²	1	1	yes	characteristic
29	C₅×#803	C₂²	1	2	yes	—
30	C₅×#803	C₂²	1	2	yes	—
31	#83286	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#135	—	3	4	no	—
33	C₅×#532	—	3	1	no	—
34	C₅×#532	D₃	1	1	yes	characteristic, complemented
35	C₅×#497	—	3	2	no	—
36	C₅×#497	—	3	2	no	—
37	C₅×#496	—	3	2	no	—
38	C₅×#496	—	3	2	no	—
39	C₂×C₅×#97	—	3	1	no	—
40	C₃×C₅×#41	—	2	8	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×#67	—	2	2	no	—
49	C₅×#235	—	2	8	no	—
50	C₂×C₅×D₁₂	—	2	2	no	—
51	C₂×C₅×D₁₂	C₂³	1	2	yes	—
52	C₂×C₄×C₅×D₃	—	2	2	no	—
53	C₂×C₅×Dic₆	C₂³	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₄²×C₅	D₄	1	2	yes	—
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₅×#216	—	2	8	no	—
60	C₅×#215	—	2	8	no	—
61	C₅×#214	—	2	8	no	—
62	C₅×#213	—	2	8	no	—
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×C₄⋊Dic₃	—	2	2	no	—
65	C₂×C₅×C₃⋊C₈	D₄	1	8	yes	complemented
66	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
67	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#950	C₂×C₅	1	4	yes	complemented
69	#5477	C₂×C₅	1	1	yes	characteristic, complemented
70	#5086	C₂×C₅	1	2	yes	complemented
71	#5074	C₂×C₅	1	2	yes	complemented
72	#5060	C₂×C₅	1	2	yes	complemented
73	#5058	C₂×C₅	1	2	yes	complemented
74	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×C₅×#41	—	3	2	no	—
76	C₂×C₅×#41	C₂×D₃	1	2	yes	—
77	C₅×#135	—	6	16	no	—
78	C₂×C₅×Q₁₆	—	3	4	no	—
79	C₂×C₅×SD₁₆	—	3	4	no	—
80	C₂×C₅×SD₁₆	—	3	4	no	—
81	C₂×C₅×D₈	—	3	4	no	—
82	C₂²×C₅×C₈	—	3	2	no	—
83	C₅×C₄⋊Q₈	—	3	1	no	—
84	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
85	C₅×#127	—	3	1	no	—
86	C₅×#127	C₂×D₃	1	1	yes	characteristic
87	C₅×#124	—	3	2	no	—
88	C₅×#124	C₂×D₃	1	2	yes	—
89	C₅×#121	—	2	2	no	—
90	C₅×#121	—	6	2	no	—
91	C₄×C₅×D₄	—	2	2	no	—
92	C₄×C₅×D₄	—	6	2	no	—
93	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
94	C₅×#97	—	3	2	no	—
95	C₅×#97	—	3	2	no	—
96	#3150	—	3	1	no	Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	2	no	—
100	C₃×C₅×Q₈	—	2	4	no	—
101	C₃×C₅×D₄	—	2	4	no	—
102	C₃×C₅×D₄	—	4	4	no	—
103	C₃×C₅×D₄	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	4	2	no	—
106	C₂×C₃×C₄×C₅	—	4	4	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₅×#67	—	4	4	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₅×D₁₂	—	2	4	no	—
115	C₅×D₁₂	—	4	4	no	—
116	C₄×C₅×D₃	—	4	4	no	—
117	C₅×Dic₆	—	2	4	no	—
118	C₅×C₃⋊C₈	C₂×D₄	1	8	yes	—
119	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
120	C₂×#235	C₂²×C₅	1	2	yes	—
121	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
122	C₃×#127	C₂²×C₅	1	1	yes	characteristic
123	C₃×#124	C₂²×C₅	1	2	yes	—
124	C₃×#121	—	2	2	no	—
125	C₃×C₄×D₄	—	2	2	no	—
126	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
127	#950	—	2	16	no	—
128	C₂×#216	C₂²×C₅	1	4	yes	—
129	C₂×#215	C₂²×C₅	1	4	yes	—
130	C₂×#214	C₂²×C₅	1	4	yes	—
131	C₂×#213	C₂²×C₅	1	4	yes	—
132	#930	—	2	2	no	—
133	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
134	#875	C₂²×C₅	1	2	yes	—
135	#874	C₂²×C₅	1	1	yes	characteristic
136	C₄×D₁₂	—	2	2	no	—
137	#869	C₂²×C₅	1	1	yes	characteristic
138	#803	C₂²×C₅	1	2	yes	—
139	#803	C₂²×C₅	1	2	yes	—
140	C₅×#41	—	2	8	no	—
141	C₅×#41	—	6	8	no	—
142	C₂×C₅×Q₈	—	3	2	no	—
143	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	3	2	no	—
147	C₂×C₅×D₄	—	6	2	no	—
148	C₂×C₅×D₄	—	6	2	no	—
149	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	6	2	no	—
152	C₂²×C₄×C₅	#67	1	2	yes	—
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₅×Q₁₆	—	6	8	no	—
155	C₅×SD₁₆	—	6	8	no	—
156	C₅×SD₁₆	—	6	8	no	—
157	C₅×D₈	—	6	8	no	—
158	C₂×C₅×C₈	—	3	8	no	—
159	C₂×C₅×C₈	—	3	4	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	6	2	no	—
162	C₅×C₂²⋊C₄	—	2	4	no	—
163	C₅×C₂²⋊C₄	—	6	4	no	—
164	C₄²×C₅	#67	1	2	yes	—
165	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₂×#135	—	3	4	no	—
168	#532	—	3	1	no	—
169	#532	C₅×D₃	1	1	yes	characteristic, complemented
170	#497	—	3	2	no	—
171	#497	—	3	2	no	—
172	#496	—	3	2	no	—
173	#496	—	3	2	no	—
174	C₂×#97	—	3	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	4	no	—
178	C₂²×C₃×C₅	#127	1	2	yes	—
179	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₅×D₃	—	4	2	no	—
181	C₂×C₅×D₃	—	4	4	no	—
182	C₃×C₄×C₅	—	2	2	no	—
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	#127	1	2	yes	—
186	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
187	C₅×Dic₃	—	4	2	no	—
188	C₃×#41	—	2	8	no	—
189	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	2	no	—
192	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
193	C₂²×C₃×C₄	—	2	2	no	—
194	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂×#67	—	2	2	no	—
197	#235	—	2	8	no	—
198	C₂×D₁₂	—	2	2	no	—
199	C₂×D₁₂	C₂³×C₅	1	2	yes	—
200	C₂×C₄×D₃	—	2	2	no	—
201	C₂×Dic₆	C₂³×C₅	1	2	yes	—
202	C₃×C₄⋊C₄	—	2	2	no	—
203	C₃×C₂²⋊C₄	—	2	4	no	—
204	C₃×C₄²	C₅×D₄	1	2	yes	—
205	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
206	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
207	#216	—	2	8	no	—
208	#215	—	2	8	no	—
209	#214	—	2	8	no	—
210	#213	—	2	8	no	—
211	(C₂×D₃)⋊C₄	—	2	4	no	—
212	C₄⋊Dic₃	—	2	2	no	—
213	C₂×C₃⋊C₈	C₅×D₄	1	8	yes	complemented
214	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	6	2	no	—
217	C₂³×C₅	C₂×#67	1	1	yes	characteristic
218	C₅×Q₈	—	2	4	no	—
219	C₅×Q₈	—	6	4	no	—
220	C₅×D₄	—	2	4	no	—
221	C₅×D₄	—	4	4	no	—
222	C₅×D₄	—	4	4	no	—
223	C₅×D₄	—	6	4	no	—
224	C₅×D₄	—	12	4	no	—
225	C₅×D₄	—	12	4	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	4	no	—
229	C₂×C₄×C₅	—	6	2	no	—
230	C₂×C₄×C₅	—	12	4	no	—
231	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
232	C₂×C₄×C₅	C₂×#67	1	2	yes	—
233	C₂×C₄×C₅	C₂×#67	1	2	yes	—
234	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
236	C₅×C₈	—	3	8	no	—
237	C₂×#41	—	3	2	no	—
238	C₂×#41	C₂×C₅×D₃	1	2	yes	—
239	#135	—	6	16	no	—
240	C₂×Q₁₆	—	3	4	no	—
241	C₂×SD₁₆	—	3	4	no	—
242	C₂×SD₁₆	—	3	4	no	—
243	C₂×D₈	—	3	4	no	—
244	C₂²×C₈	—	3	2	no	—
245	C₄⋊Q₈	—	3	1	no	—
246	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
247	#127	—	3	1	no	—
248	#127	C₂×C₅×D₃	1	1	yes	characteristic
249	#124	—	3	2	no	—
250	#124	C₂×C₅×D₃	1	2	yes	—
251	#121	—	2	2	no	—
252	#121	—	6	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	6	2	no	—
255	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
256	#97	—	3	2	no	—
257	#97	—	3	2	no	—
258	C₂×C₃×C₅	—	2	2	no	—
259	C₂×C₃×C₅	—	8	2	no	—
260	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
261	C₂×C₃×C₅	#575	1	2	yes	—
262	C₅×D₃	—	8	2	no	—
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂²×D₃	—	2	2	no	—
266	C₃×Q₈	—	2	4	no	—
267	C₃×D₄	—	2	4	no	—
268	C₃×D₄	—	4	4	no	—
269	C₃×D₄	—	4	4	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	4	no	—
273	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
274	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
276	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
278	#67	—	4	4	no	—
279	C₂×Dic₃	—	2	2	no	—
280	D₁₂	—	2	4	no	—
281	D₁₂	—	4	4	no	—
282	C₄×D₃	—	4	4	no	—
283	Dic₆	—	2	4	no	—
284	C₃⋊C₈	C₂×C₅×D₄	1	8	yes	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	4	4	no	—
288	C₂²×C₅	—	12	2	no	—
289	C₂²×C₅	—	12	4	no	—
290	C₂²×C₅	#940	1	2	yes	—
291	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	12	2	no	—
296	C₄×C₅	#940	1	2	yes	—
297	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
298	#41	—	2	8	no	—
299	#41	—	6	8	no	—
300	C₂×Q₈	—	3	2	no	—
301	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	3	2	no	—
305	C₂×D₄	—	6	2	no	—
306	C₂×D₄	—	6	2	no	—
307	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	6	2	no	—
310	C₂²×C₄	C₅×#67	1	2	yes	—
311	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
312	Q₁₆	—	6	8	no	—
313	SD₁₆	—	6	8	no	—
314	SD₁₆	—	6	8	no	—
315	D₈	—	6	8	no	—
316	C₂×C₈	—	3	8	no	—
317	C₂×C₈	—	3	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	6	2	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	6	4	no	—
322	C₄²	C₅×#67	1	2	yes	—
323	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
324	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
325	C₃×C₅	#3150	1	1	yes	characteristic, complemented, Hall
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	4	2	no	—
328	C₂²×C₃	—	4	4	no	—
329	C₂²×C₃	C₅×#127	1	2	yes	—
330	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
331	C₂×D₃	—	4	2	no	—
332	C₂×D₃	—	4	4	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	C₅×#127	1	2	yes	—
337	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
338	Dic₃	—	4	2	no	—
339	C₂×C₅	—	2	2	no	—
340	C₂×C₅	—	8	2	no	—
341	C₂×C₅	—	24	2	no	—
342	C₂×C₅	C₂×#940	1	1	yes	characteristic
343	C₂×C₅	#5822	1	2	yes	—
344	C₂³	—	2	2	no	—
345	C₂³	—	6	2	no	—
346	C₂³	C₂×C₅×#67	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	6	4	no	—
349	D₄	—	2	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	6	4	no	—
353	D₄	—	12	4	no	—
354	D₄	—	12	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	—	12	4	no	—
360	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
361	C₂×C₄	C₂×C₅×#67	1	2	yes	—
362	C₂×C₄	C₂×C₅×#67	1	2	yes	—
363	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
364	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
365	C₈	—	3	8	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	8	2	no	—
368	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
369	C₂×C₃	C₅×#575	1	2	yes	—
370	D₃	—	8	2	no	—
371	C₅	#83286	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	12	2	no	—
376	C₂²	—	12	4	no	—
377	C₂²	C₅×#940	1	2	yes	—
378	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	12	2	no	—
383	C₄	C₅×#940	1	2	yes	—
384	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
385	C₃	C₅×#3150	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	2	2	no	—
387	C₂	—	8	2	no	—
388	C₂	—	24	2	no	—
389	C₂	C₂×C₅×#940	1	1	yes	characteristic
390	C₂	C₅×#5822	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#3150
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₂×C₅×#950	C₂	semidirect
3. C₅×#5477	C₂	semidirect
4. C₅×#5086	C₂	semidirect
5. C₅×#5074	C₂	semidirect
6. C₅×#5060	C₂	semidirect
7. C₅×#5058	C₂	semidirect
8. C₂×C₅×#803	C₂	semidirect
31. #83286	C₅	direct (N × H)
34. C₅×#532	D₃	semidirect
65. C₂×C₅×C₃⋊C₈	D₄	semidirect
67. C₃×#532	C₂×C₅	semidirect
68. C₂×#950	C₂×C₅	semidirect
69. #5477	C₂×C₅	semidirect
70. #5086	C₂×C₅	semidirect
71. #5074	C₂×C₅	semidirect
72. #5060	C₂×C₅	semidirect
73. #5058	C₂×C₅	semidirect
74. C₂×#803	C₂×C₅	semidirect
169. #532	C₅×D₃	semidirect
213. C₂×C₃⋊C₈	C₅×D₄	semidirect
325. C₃×C₅	#3150	semidirect
371. C₅	#83286	direct (N × H)
385. C₃	C₅×#3150	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
C₂×C₅×#950	2
C₅×#5477	2
C₅×#5086	2
C₅×#5074	2
C₅×#5060	2
C₅×#5058	2
C₂×C₅×#803	2
C₅×#3150	3
#83286	5

Subgroups — C5×#83286 #14439078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83286 #14439078