Subgroups — C₅×#68989 #14294773

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#343	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4554	C₂	1	2	yes	maximal, complemented
5	C₅×#4530	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1742	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
11	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Dic₃	C₄	1	2	yes	—
13	C₂×C₅×#208	C₂²	1	2	yes	—
14	C₅×D₃×M₁₆	—	2	4	no	—
15	C₅×D₃×M₁₆	C₄	1	8	yes	complemented
16	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
17	C₂×C₅×D₃×C₈	—	2	2	no	—
18	C₅×#892	—	2	2	no	—
19	C₅×#892	—	2	2	no	—
20	#68989	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×M₁₆	—	3	2	no	—
22	C₂×C₅×#117	—	3	1	no	—
23	C₅×#343	—	3	2	no	—
24	C₅×#343	—	3	1	no	—
25	C₅×#343	D₃	1	1	yes	characteristic, complemented
26	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
28	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
30	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
32	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
33	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
34	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
35	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
36	C₃×C₅×M₁₆	—	2	2	no	—
37	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₃×C₅×C₄⋊C₄	—	2	2	no	—
40	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
41	C₅×C₄⋊Dic₃	—	2	2	no	—
42	C₄×C₅×Dic₃	—	2	2	no	—
43	C₄×C₅×Dic₃	—	2	2	no	—
44	C₅×#208	—	2	2	no	—
45	C₅×#208	C₂×C₄	1	4	yes	—
46	C₂×C₅×C₃⋊C₈	—	2	2	no	—
47	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
48	C₅×D₃×C₈	—	2	8	no	—
49	C₂×D₃×M₁₆	C₂×C₅	1	2	yes	—
50	C₂×#892	C₂×C₅	1	1	yes	characteristic
51	C₃×#343	C₂×C₅	1	1	yes	characteristic, complemented
52	#4554	C₂×C₅	1	2	yes	complemented
53	#4530	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂³×C₄×C₅	—	3	1	no	—
55	C₂×C₅×M₁₆	—	3	2	no	—
56	C₂×C₅×M₁₆	—	3	8	no	—
57	C₂×C₅×M₁₆	—	6	2	no	—
58	C₂×C₅×M₁₆	—	6	4	no	—
59	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
60	C₂²×C₅×C₈	—	6	2	no	—
61	C₅×#117	—	6	2	no	—
62	C₅×#117	—	6	2	no	—
63	C₂×C₅×C₄⋊C₄	—	3	1	no	—
64	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
65	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
66	C₂×C₄²×C₅	—	3	2	no	—
67	#1742	—	3	1	no	Sylow
68	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₅×D₃	—	4	1	no	—
70	C₂²×C₅×D₃	—	4	1	no	—
71	C₂²×C₅×D₃	C₄²	1	2	yes	—
72	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
73	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
74	C₂×C₃×C₄×C₅	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	4	2	no	—
76	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
80	C₂×C₅×Dic₃	—	2	2	no	—
81	C₂×C₅×Dic₃	—	4	2	no	—
82	C₂×C₅×Dic₃	C₄²	1	2	yes	—
83	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
86	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
87	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
88	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
89	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
90	C₃×C₅×C₈	—	2	4	no	—
91	C₅×C₃⋊C₈	—	2	4	no	—
92	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
94	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
95	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
96	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
97	C₂×C₄×Dic₃	C₄×C₅	1	2	yes	—
98	C₂×#208	C₂²×C₅	1	2	yes	—
99	D₃×M₁₆	—	2	4	no	—
100	D₃×M₁₆	C₄×C₅	1	8	yes	complemented
101	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
102	C₂×D₃×C₈	—	2	2	no	—
103	#892	—	2	2	no	—
104	#892	—	2	2	no	—
105	C₂⁴×C₅	—	3	1	no	—
106	C₂²×C₄×C₅	—	3	1	no	—
107	C₂²×C₄×C₅	—	3	4	no	—
108	C₂²×C₄×C₅	—	3	2	no	—
109	C₂²×C₄×C₅	—	3	2	no	—
110	C₂²×C₄×C₅	—	3	2	no	—
111	C₂²×C₄×C₅	—	3	2	no	—
112	C₂²×C₄×C₅	—	3	2	no	—
113	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
114	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
115	C₅×M₁₆	—	2	2	no	—
116	C₅×M₁₆	—	3	4	no	—
117	C₅×M₁₆	—	6	8	no	—
118	C₅×M₁₆	—	6	2	no	—
119	C₅×M₁₆	C₄×D₃	1	4	yes	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	6	8	no	—
122	C₂×C₅×C₈	—	6	2	no	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₄⋊C₄	—	6	2	no	—
125	C₅×C₂²⋊C₄	—	6	4	no	—
126	C₄²×C₅	—	6	2	no	—
127	C₄²×C₅	—	6	2	no	—
128	C₂²×M₁₆	—	3	2	no	—
129	C₂×#117	—	3	1	no	—
130	#343	—	3	2	no	—
131	#343	—	3	1	no	—
132	#343	C₅×D₃	1	1	yes	characteristic, complemented
133	C₂²×C₃×C₅	—	2	1	no	—
134	C₂²×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
136	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₅×D₃	—	2	2	no	—
139	C₂×C₅×D₃	—	2	2	no	—
140	C₂×C₅×D₃	—	4	2	no	—
141	C₂×C₅×D₃	—	4	2	no	—
142	C₂×C₅×D₃	#95	1	4	yes	—
143	C₃×C₄×C₅	—	4	2	no	—
144	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
145	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
146	C₅×Dic₃	—	4	2	no	—
147	C₅×Dic₃	#95	1	2	yes	—
148	C₅×Dic₃	#95	1	2	yes	—
149	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
151	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
152	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
153	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
154	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
155	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
156	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
157	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
158	C₂×C₄×D₃	C₅×Q₈	1	2	yes	—
159	C₃×M₁₆	—	2	2	no	—
160	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₃×C₄⋊C₄	—	2	2	no	—
163	(C₂×D₃)⋊C₄	—	2	4	no	—
164	C₄⋊Dic₃	—	2	2	no	—
165	C₄×Dic₃	—	2	2	no	—
166	C₄×Dic₃	—	2	2	no	—
167	#208	—	2	2	no	—
168	#208	C₂×C₄×C₅	1	4	yes	—
169	C₂×C₃⋊C₈	—	2	2	no	—
170	ΓL(1,𝔽₂₅)	—	2	8	no	—
171	D₃×C₈	—	2	8	no	—
172	C₂³×C₅	—	3	2	no	—
173	C₂³×C₅	—	3	2	no	—
174	C₂³×C₅	—	3	2	no	—
175	C₂³×C₅	—	12	1	no	—
176	C₂³×C₅	—	12	1	no	—
177	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	3	2	no	—
180	C₂×C₄×C₅	—	3	1	no	—
181	C₂×C₄×C₅	—	3	1	no	—
182	C₂×C₄×C₅	—	3	2	no	—
183	C₂×C₄×C₅	—	3	4	no	—
184	C₂×C₄×C₅	—	3	4	no	—
185	C₂×C₄×C₅	—	3	4	no	—
186	C₂×C₄×C₅	—	3	4	no	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	—	6	2	no	—
189	C₂×C₄×C₅	—	12	2	no	—
190	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
191	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
193	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
194	C₅×C₈	—	2	4	no	—
195	C₅×C₈	—	6	4	no	—
196	C₂³×C₄	—	3	1	no	—
197	C₂×M₁₆	—	3	2	no	—
198	C₂×M₁₆	—	3	8	no	—
199	C₂×M₁₆	—	6	2	no	—
200	C₂×M₁₆	—	6	4	no	—
201	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
202	C₂²×C₈	—	6	2	no	—
203	#117	—	6	2	no	—
204	#117	—	6	2	no	—
205	C₂×C₄⋊C₄	—	3	1	no	—
206	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	—	3	2	no	—
208	C₂×C₄²	—	3	2	no	—
209	C₂×C₃×C₅	—	2	1	no	—
210	C₂×C₃×C₅	—	2	1	no	—
211	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
212	C₂×C₃×C₅	#413	1	1	yes	characteristic
213	C₂×C₃×C₅	#413	1	1	yes	characteristic
214	C₅×D₃	—	2	4	no	—
215	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
216	C₂²×D₃	—	4	1	no	—
217	C₂²×D₃	—	4	1	no	—
218	C₂²×D₃	C₄²×C₅	1	2	yes	—
219	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
220	C₂²×D₃	C₅×C₄⋊C₄	1	2	yes	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	4	2	no	—
223	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
226	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
227	C₂×Dic₃	—	2	2	no	—
228	C₂×Dic₃	—	4	2	no	—
229	C₂×Dic₃	C₄²×C₅	1	2	yes	—
230	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×Dic₃	C₅×C₄⋊C₄	1	2	yes	—
233	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
234	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
235	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
236	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
237	C₃×C₈	—	2	4	no	—
238	C₃⋊C₈	—	2	4	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	3	4	no	—
242	C₂²×C₅	—	6	2	no	—
243	C₂²×C₅	—	6	2	no	—
244	C₂²×C₅	—	12	2	no	—
245	C₂²×C₅	—	12	2	no	—
246	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
247	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
249	C₄×C₅	—	3	2	no	—
250	C₄×C₅	—	3	2	no	—
251	C₄×C₅	—	4	2	no	—
252	C₄×C₅	—	12	2	no	—
253	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
254	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
255	C₂⁴	—	3	1	no	—
256	C₂²×C₄	—	3	1	no	—
257	C₂²×C₄	—	3	4	no	—
258	C₂²×C₄	—	3	2	no	—
259	C₂²×C₄	—	3	2	no	—
260	C₂²×C₄	—	3	2	no	—
261	C₂²×C₄	—	3	2	no	—
262	C₂²×C₄	—	3	2	no	—
263	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
264	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
265	M₁₆	—	2	2	no	—
266	M₁₆	—	3	4	no	—
267	M₁₆	—	6	8	no	—
268	M₁₆	—	6	2	no	—
269	M₁₆	C₄×C₅×D₃	1	4	yes	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	6	8	no	—
272	C₂×C₈	—	6	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	6	2	no	—
275	C₂²⋊C₄	—	6	4	no	—
276	C₄²	—	6	2	no	—
277	C₄²	—	6	2	no	—
278	C₃×C₅	#1742	1	1	yes	characteristic, complemented, Hall
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
282	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
284	C₂×D₃	—	2	2	no	—
285	C₂×D₃	—	2	2	no	—
286	C₂×D₃	—	4	2	no	—
287	C₂×D₃	—	4	2	no	—
288	C₂×D₃	C₅×#95	1	4	yes	—
289	C₃×C₄	—	4	2	no	—
290	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
291	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
292	Dic₃	—	4	2	no	—
293	Dic₃	C₅×#95	1	2	yes	—
294	Dic₃	C₅×#95	1	2	yes	—
295	C₂×C₅	—	2	1	no	—
296	C₂×C₅	—	2	1	no	—
297	C₂×C₅	—	6	4	no	—
298	C₂×C₅	D₃×#95	1	1	yes	characteristic
299	C₂×C₅	#4745	1	1	yes	characteristic
300	C₂×C₅	#4751	1	1	yes	characteristic
301	C₂³	—	3	2	no	—
302	C₂³	—	3	2	no	—
303	C₂³	—	3	2	no	—
304	C₂³	—	12	1	no	—
305	C₂³	—	12	1	no	—
306	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	3	2	no	—
309	C₂×C₄	—	3	1	no	—
310	C₂×C₄	—	3	1	no	—
311	C₂×C₄	—	3	2	no	—
312	C₂×C₄	—	3	4	no	—
313	C₂×C₄	—	3	4	no	—
314	C₂×C₄	—	3	4	no	—
315	C₂×C₄	—	3	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	6	2	no	—
318	C₂×C₄	—	12	2	no	—
319	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
320	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
321	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
322	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
323	C₈	—	2	4	no	—
324	C₈	—	6	4	no	—
325	C₂×C₃	—	2	1	no	—
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	C₂×C₅×#95	1	1	yes	characteristic
328	C₂×C₃	C₅×#413	1	1	yes	characteristic
329	C₂×C₃	C₅×#413	1	1	yes	characteristic
330	D₃	—	2	4	no	—
331	C₅	#68989	1	1	yes	characteristic, direct product factor, Sylow
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	3	4	no	—
335	C₂²	—	6	2	no	—
336	C₂²	—	6	2	no	—
337	C₂²	—	12	2	no	—
338	C₂²	—	12	2	no	—
339	C₂²	C₄²×C₅×D₃	1	1	yes	characteristic
340	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
342	C₄	—	3	2	no	—
343	C₄	—	3	2	no	—
344	C₄	—	4	2	no	—
345	C₄	—	12	2	no	—
346	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
347	C₄	C₅×D₃×C₄⋊C₄	1	2	yes	—
348	C₃	C₅×#1742	1	1	yes	characteristic, complemented, Sylow
349	C₂	—	2	1	no	—
350	C₂	—	2	1	no	—
351	C₂	—	6	4	no	—
352	C₂	C₅×D₃×#95	1	1	yes	characteristic
353	C₂	C₅×#4745	1	1	yes	characteristic
354	C₂	C₅×#4751	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#343	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#343	D₃
hypocenter	C₃	C₅×#1742
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#343

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#343	C₂	semidirect
4. C₅×#4554	C₂	semidirect
5. C₅×#4530	C₂	semidirect
15. C₅×D₃×M₁₆	C₄	semidirect
20. #68989	C₅	direct (N × H)
25. C₅×#343	D₃	semidirect
51. C₃×#343	C₂×C₅	semidirect
52. #4554	C₂×C₅	semidirect
53. #4530	C₂×C₅	semidirect
100. D₃×M₁₆	C₄×C₅	semidirect
132. #343	C₅×D₃	semidirect
278. C₃×C₅	#1742	semidirect
331. C₅	#68989	direct (N × H)
348. C₃	C₅×#1742	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂×C₅×#892	2
C₃×C₅×#343	2
C₅×#4554	2
C₅×#4530	2
C₅×#1742	3
#68989	5

Subgroups — C5×#68989 #14294773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68989 #14294773