Subgroups — C₅×#82224 #14320147

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₅×#4977	C₂	1	2	yes	maximal, complemented
5	C₅×#4975	C₂	1	2	yes	maximal, complemented
6	C₅×#4942	C₂	1	4	yes	maximal
7	C₄×C₅×Dic₃⋊C₄	C₂	1	4	yes	maximal, complemented
8	C₅×#2285	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
11	C₃×C₅×#117	—	2	4	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₅×#217	C₂²	1	2	yes	—
16	C₅×#926	—	2	4	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	—
19	C₂×C₄×C₅×Dic₃	C₄	1	8	yes	complemented
20	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₅×C₃⋊#95	C₂²	1	8	yes	—
25	#82224	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#117	—	3	1	no	—
27	C₂×C₅×#117	D₃	1	1	yes	characteristic
28	C₂²×C₄²×C₅	—	3	1	no	—
29	C₅×#384	—	3	2	no	—
30	C₅×#382	—	3	2	no	—
31	C₅×#380	—	3	4	no	—
32	C₄×C₅×C₄⋊C₄	—	3	4	no	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
36	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	—	2	8	no	—
41	C₂²×C₅×Dic₃	C₂×C₄	1	8	yes	—
42	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
43	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
44	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
47	C₃×C₄²×C₅	—	2	4	no	—
48	C₅×#217	—	2	4	no	—
49	C₅×C₄⋊Dic₃	—	2	4	no	—
50	C₅×Dic₃⋊C₄	—	2	16	no	—
51	C₄×C₅×Dic₃	—	2	4	no	—
52	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
53	C₄×C₅×Dic₃	C₂×C₄	1	8	yes	—
54	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
55	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
56	C₂×#926	C₂×C₅	1	1	yes	characteristic
57	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic
58	#4977	C₂×C₅	1	2	yes	complemented
59	#4975	C₂×C₅	1	2	yes	complemented
60	#4942	C₂×C₅	1	4	yes	—
61	C₄×Dic₃⋊C₄	C₂×C₅	1	4	yes	complemented
62	C₂³×C₄×C₅	—	3	2	no	—
63	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
64	C₅×#117	—	2	4	no	—
65	C₅×#117	—	6	4	no	—
66	C₂×C₅×C₄⋊C₄	—	3	8	no	—
67	C₂×C₅×C₄⋊C₄	—	3	2	no	—
68	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
70	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
71	C₂×C₄²×C₅	—	3	8	no	—
72	C₂×C₄²×C₅	—	3	1	no	—
73	C₂×C₄²×C₅	—	3	1	no	—
74	C₂×C₄²×C₅	—	3	2	no	—
75	C₂×C₄²×C₅	—	3	2	no	—
76	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
77	C₅×#95	—	3	8	no	—
78	#2285	—	3	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
83	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	8	no	—
86	C₂×C₃×C₄×C₅	C₄⋊C₄	1	16	yes	complemented
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
93	C₂×C₅×Dic₃	—	2	4	no	—
94	C₂×C₅×Dic₃	—	2	16	no	—
95	C₂×C₅×Dic₃	—	2	4	no	—
96	C₂×C₅×Dic₃	—	2	8	no	—
97	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
98	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
99	C₂×C₅×Dic₃	#41	1	8	yes	—
100	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
101	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
102	C₃×#117	—	2	4	no	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
106	C₂×#217	C₂²×C₅	1	2	yes	—
107	#926	—	2	4	no	—
108	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
109	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	—
110	C₂×C₄×Dic₃	C₄×C₅	1	8	yes	complemented
111	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
112	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
113	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
115	C₃⋊#95	C₂²×C₅	1	8	yes	—
116	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	—	3	2	no	—
118	C₂²×C₄×C₅	—	3	8	no	—
119	C₂²×C₄×C₅	—	3	2	no	—
120	C₂²×C₄×C₅	—	3	4	no	—
121	C₂²×C₄×C₅	—	6	8	no	—
122	C₂²×C₄×C₅	Dic₆	1	4	yes	—
123	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
124	C₂²×C₄×C₅	#67	1	4	yes	—
125	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
126	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	6	16	no	—
130	C₅×C₄⋊C₄	—	6	4	no	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₅×C₂²⋊C₄	—	6	4	no	—
133	C₄²×C₅	—	2	4	no	—
134	C₄²×C₅	—	3	4	no	—
135	C₄²×C₅	—	3	8	no	—
136	C₄²×C₅	—	3	4	no	—
137	C₄²×C₅	—	6	4	no	—
138	C₂×#117	—	3	1	no	—
139	C₂×#117	C₅×D₃	1	1	yes	characteristic
140	C₂²×C₄²	—	3	1	no	—
141	#384	—	3	2	no	—
142	#382	—	3	2	no	—
143	#380	—	3	4	no	—
144	C₄×C₄⋊C₄	—	3	4	no	—
145	C₂²×C₃×C₅	—	2	4	no	—
146	C₂²×C₃×C₅	—	2	4	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
149	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
153	C₃×C₄×C₅	—	4	4	no	—
154	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
155	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
156	C₅×Dic₃	—	2	4	no	—
157	C₅×Dic₃	—	4	4	no	—
158	C₅×Dic₃	#117	1	8	yes	complemented
159	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
161	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
162	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
163	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
166	C₂²×Dic₃	—	2	8	no	—
167	C₂²×Dic₃	C₂×C₄×C₅	1	8	yes	—
168	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
169	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
170	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₂²⋊C₄	—	2	4	no	—
173	C₃×C₄²	—	2	4	no	—
174	#217	—	2	4	no	—
175	C₄⋊Dic₃	—	2	4	no	—
176	Dic₃⋊C₄	—	2	16	no	—
177	C₄×Dic₃	—	2	4	no	—
178	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
179	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	—
180	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
181	C₂³×C₅	—	2	4	no	—
182	C₂³×C₅	C₂×Dic₆	1	2	yes	—
183	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
184	C₂³×C₅	C₂×#67	1	2	yes	—
185	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
186	C₂×C₄×C₅	—	2	8	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	3	4	no	—
189	C₂×C₄×C₅	—	3	8	no	—
190	C₂×C₄×C₅	—	3	4	no	—
191	C₂×C₄×C₅	—	6	16	no	—
192	C₂×C₄×C₅	—	6	4	no	—
193	C₂×C₄×C₅	—	6	8	no	—
194	C₂×C₄×C₅	—	6	4	no	—
195	C₂×C₄×C₅	Dic₃⋊C₄	1	16	yes	complemented
196	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
197	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
198	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
200	C₂×C₄×C₅	C₂×#67	1	2	yes	—
201	C₂×C₄×C₅	C₂×#67	1	2	yes	—
202	C₂³×C₄	—	3	2	no	—
203	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
204	#117	—	2	4	no	—
205	#117	—	6	4	no	—
206	C₂×C₄⋊C₄	—	3	2	no	—
207	C₂×C₄⋊C₄	—	3	8	no	—
208	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
209	C₂×C₂²⋊C₄	—	3	2	no	—
210	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
211	C₂×C₄²	—	3	8	no	—
212	C₂×C₄²	—	3	2	no	—
213	C₂×C₄²	—	3	1	no	—
214	C₂×C₄²	—	3	1	no	—
215	C₂×C₄²	—	3	2	no	—
216	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
217	#95	—	3	8	no	—
218	C₂×C₃×C₅	—	2	4	no	—
219	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₃×C₅	C₂×#117	1	2	yes	—
221	C₂×C₃×C₅	#532	1	2	yes	—
222	C₂×C₃×C₅	#533	1	2	yes	—
223	C₂³×C₃	—	2	4	no	—
224	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
225	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
226	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
227	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	8	no	—
230	C₂×C₃×C₄	C₅×C₄⋊C₄	1	16	yes	complemented
231	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
232	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
233	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
234	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
236	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
237	C₂×Dic₃	—	2	4	no	—
238	C₂×Dic₃	—	2	16	no	—
239	C₂×Dic₃	—	2	4	no	—
240	C₂×Dic₃	—	2	8	no	—
241	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
242	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
243	C₂×Dic₃	C₅×#41	1	8	yes	—
244	C₂²×C₅	—	2	4	no	—
245	C₂²×C₅	—	2	4	no	—
246	C₂²×C₅	—	2	4	no	—
247	C₂²×C₅	C₂×Dic₃⋊C₄	1	4	yes	—
248	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
249	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
250	C₂²×C₅	D₃×#41	1	4	yes	—
251	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
252	C₄×C₅	—	3	8	no	—
253	C₄×C₅	—	4	4	no	—
254	C₄×C₅	—	6	4	no	—
255	C₄×C₅	—	12	4	no	—
256	C₄×C₅	C₂×Dic₃⋊C₄	1	4	yes	—
257	C₄×C₅	C₂×Dic₃⋊C₄	1	4	yes	—
258	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
259	C₂²×C₄	—	3	2	no	—
260	C₂²×C₄	—	3	8	no	—
261	C₂²×C₄	—	3	2	no	—
262	C₂²×C₄	—	3	4	no	—
263	C₂²×C₄	—	6	8	no	—
264	C₂²×C₄	C₅×Dic₆	1	4	yes	—
265	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
266	C₂²×C₄	C₅×#67	1	4	yes	—
267	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
268	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	6	16	no	—
272	C₄⋊C₄	—	6	4	no	—
273	C₂²⋊C₄	—	2	4	no	—
274	C₂²⋊C₄	—	6	4	no	—
275	C₄²	—	2	4	no	—
276	C₄²	—	3	4	no	—
277	C₄²	—	3	8	no	—
278	C₄²	—	3	4	no	—
279	C₄²	—	6	4	no	—
280	C₃×C₅	#2285	1	1	yes	characteristic, complemented, Hall
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	—	2	4	no	—
283	C₂²×C₃	—	2	4	no	—
284	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
285	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
286	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
287	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
288	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
289	C₃×C₄	—	4	4	no	—
290	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
291	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
292	Dic₃	—	2	4	no	—
293	Dic₃	—	4	4	no	—
294	Dic₃	C₅×#117	1	8	yes	complemented
295	C₂×C₅	—	2	4	no	—
296	C₂×C₅	#5517	1	2	yes	—
297	C₂×C₅	D₃×#117	1	2	yes	—
298	C₂×C₅	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
299	C₂×C₅	#5832	1	2	yes	—
300	C₂³	—	2	4	no	—
301	C₂³	C₂×C₅×Dic₆	1	2	yes	—
302	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
303	C₂³	C₂×C₅×#67	1	2	yes	—
304	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	3	4	no	—
308	C₂×C₄	—	3	8	no	—
309	C₂×C₄	—	3	4	no	—
310	C₂×C₄	—	6	16	no	—
311	C₂×C₄	—	6	4	no	—
312	C₂×C₄	—	6	8	no	—
313	C₂×C₄	—	6	4	no	—
314	C₂×C₄	C₅×Dic₃⋊C₄	1	16	yes	complemented
315	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
316	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
317	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
318	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
319	C₂×C₄	C₂×C₅×#67	1	2	yes	—
320	C₂×C₄	C₂×C₅×#67	1	2	yes	—
321	C₂×C₃	—	2	4	no	—
322	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₃	C₂×C₅×#117	1	2	yes	—
324	C₂×C₃	C₅×#532	1	2	yes	—
325	C₂×C₃	C₅×#533	1	2	yes	—
326	C₅	#82224	1	1	yes	characteristic, direct product factor, Sylow
327	C₂²	—	2	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	C₂×C₅×Dic₃⋊C₄	1	4	yes	—
331	C₂²	C₂²×C₅×Dic₆	1	1	yes	characteristic
332	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
333	C₂²	C₅×D₃×#41	1	4	yes	—
334	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
335	C₄	—	3	8	no	—
336	C₄	—	4	4	no	—
337	C₄	—	6	4	no	—
338	C₄	—	12	4	no	—
339	C₄	C₂×C₅×Dic₃⋊C₄	1	4	yes	—
340	C₄	C₂×C₅×Dic₃⋊C₄	1	4	yes	—
341	C₃	C₅×#2285	1	1	yes	characteristic, complemented, Sylow
342	C₂	—	2	4	no	—
343	C₂	C₅×#5517	1	2	yes	—
344	C₂	C₅×D₃×#117	1	2	yes	—
345	C₂	C₂²×C₅×Dic₃⋊C₄	1	1	yes	characteristic
346	C₂	C₅×#5832	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#2285
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
4. C₅×#4977	C₂	semidirect
5. C₅×#4975	C₂	semidirect
7. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
19. C₂×C₄×C₅×Dic₃	C₄	semidirect
25. #82224	C₅	direct (N × H)
58. #4977	C₂×C₅	semidirect
59. #4975	C₂×C₅	semidirect
61. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
86. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
110. C₂×C₄×Dic₃	C₄×C₅	semidirect
158. C₅×Dic₃	#117	semidirect
195. C₂×C₄×C₅	Dic₃⋊C₄	semidirect
230. C₂×C₃×C₄	C₅×C₄⋊C₄	semidirect
280. C₃×C₅	#2285	semidirect
294. Dic₃	C₅×#117	semidirect
314. C₂×C₄	C₅×Dic₃⋊C₄	semidirect
326. C₅	#82224	direct (N × H)
341. C₃	C₅×#2285	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#117	2
C₂×C₅×#926	2
C₂²×C₄×C₅×Dic₃	2
C₅×#4977	2
C₅×#4975	2
C₅×#4942	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#2285	3
#82224	5

Subgroups — C5×#82224 #14320147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82224 #14320147