Subgroups — C₅×#82546 #14411971

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1004	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5798	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5006	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#806	C₂	1	8	yes	maximal, complemented
6	C₅×#2883	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₂²×C₅×#67	C₂²	1	4	yes	—
9	C₅×#1004	—	2	4	no	—
10	C₅×#1004	—	2	4	no	—
11	C₂×C₅×#237	C₄	1	4	yes	complemented
12	C₂×C₅×D₃×D₄	C₄	1	4	yes	complemented
13	C₂×C₅×#235	C₂²	1	2	yes	—
14	C₃×C₄×C₅×D₄	—	2	4	no	—
15	C₃×C₅×#117	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₅×#217	C₂²	1	4	yes	complemented
18	C₅×D₄×Dic₃	—	2	4	no	—
19	C₅×#926	C₂²	1	2	yes	complemented
20	C₅×#806	C₂²	1	16	yes	complemented
21	#82546	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
23	C₅×#518	—	3	1	no	—
24	C₅×#518	D₃	1	1	yes	characteristic, complemented
25	C₅×#410	—	3	4	no	—
26	C₂×C₅×#99	—	3	8	no	—
27	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
28	C₂³×C₅×D₃	C₂×C₄	1	4	yes	complemented
29	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
30	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
31	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
32	C₂²×C₃×C₄×C₅	—	2	4	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₅×#67	—	2	8	no	—
35	C₂×C₅×#67	—	2	8	no	—
36	C₂×C₅×#67	C₂×C₄	1	8	yes	complemented
37	C₂×C₅×#67	C₂³	1	4	yes	—
38	C₂²×C₅×Dic₃	—	2	4	no	—
39	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
40	C₅×#237	—	2	16	no	—
41	C₅×D₃×D₄	—	2	16	no	—
42	C₅×#235	—	2	4	no	—
43	C₅×#235	—	2	4	no	—
44	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	complemented
45	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
46	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	complemented
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
49	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
50	C₃×C₄²×C₅	—	2	2	no	—
51	C₅×#217	—	2	4	no	—
52	C₅×#217	C₂³	1	4	yes	—
53	C₅×C₄⋊Dic₃	—	2	2	no	—
54	C₄×C₅×Dic₃	—	2	2	no	—
55	C₂×#1004	C₂×C₅	1	1	yes	characteristic
56	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
57	#5798	C₂×C₅	1	1	yes	characteristic, complemented
58	#5006	C₂×C₅	1	4	yes	complemented
59	C₂×#806	C₂×C₅	1	8	yes	complemented
60	C₅×H(5,𝔽₂)	—	6	4	no	—
61	C₅×H(5,𝔽₂)	—	6	4	no	—
62	C₂×C₅×#41	—	3	4	no	—
63	C₂×C₅×#41	—	3	2	no	—
64	C₂²×C₅×D₄	—	3	4	no	—
65	C₂²×C₅×D₄	—	3	4	no	—
66	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
67	C₄×C₅×D₄	—	2	4	no	—
68	C₄×C₅×D₄	—	6	4	no	—
69	C₅×#117	—	3	2	no	—
70	C₅×#117	C₂×D₃	1	2	yes	complemented
71	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
72	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
73	C₅×#99	—	3	16	no	—
74	#2883	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	8	2	no	—
76	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
77	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
78	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
79	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
80	C₂²×C₅×D₃	—	2	8	no	—
81	C₂²×C₅×D₃	—	8	4	no	—
82	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
83	C₃×C₅×D₄	C₂²⋊C₄	1	16	yes	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	8	4	no	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₅×#67	—	2	16	no	—
90	C₅×#67	—	2	4	no	—
91	C₅×#67	—	2	4	no	—
92	C₂×C₅×Dic₃	—	2	8	no	—
93	C₂×C₅×Dic₃	—	2	4	no	—
94	C₂×C₅×Dic₃	—	8	4	no	—
95	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
96	C₅×D₁₂	—	2	4	no	—
97	C₄×C₅×D₃	—	2	8	no	—
98	C₅×Dic₆	—	2	4	no	—
99	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
100	C₂²×#67	C₂²×C₅	1	4	yes	—
101	#1004	—	2	4	no	—
102	#1004	—	2	4	no	—
103	C₂×#237	C₄×C₅	1	4	yes	complemented
104	C₂×D₃×D₄	C₄×C₅	1	4	yes	complemented
105	C₂×#235	C₂²×C₅	1	2	yes	—
106	C₃×C₄×D₄	—	2	4	no	—
107	C₃×#117	C₂²×C₅	1	2	yes	complemented
108	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
109	C₂×#217	C₂²×C₅	1	4	yes	complemented
110	D₄×Dic₃	—	2	4	no	—
111	#926	C₂²×C₅	1	2	yes	complemented
112	#806	C₂²×C₅	1	16	yes	complemented
113	C₂⁴×C₅	—	3	4	no	—
114	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
115	C₅×#41	—	6	16	no	—
116	C₅×#41	—	6	4	no	—
117	C₅×#41	—	6	4	no	—
118	C₂×C₅×Q₈	—	3	2	no	—
119	C₂×C₅×D₄	—	3	8	no	—
120	C₂×C₅×D₄	—	3	4	no	—
121	C₂×C₅×D₄	—	3	2	no	—
122	C₂×C₅×D₄	—	6	8	no	—
123	C₂×C₅×D₄	—	6	8	no	—
124	C₂×C₅×D₄	—	6	16	no	—
125	C₂×C₅×D₄	C₄×D₃	1	4	yes	—
126	C₂×C₅×D₄	D₁₂	1	4	yes	—
127	C₂×C₅×D₄	#67	1	4	yes	—
128	C₂²×C₄×C₅	—	2	4	no	—
129	C₂²×C₄×C₅	—	3	4	no	—
130	C₂²×C₄×C₅	—	3	4	no	—
131	C₂²×C₄×C₅	—	6	4	no	—
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	6	2	no	—
135	C₅×C₂²⋊C₄	—	2	4	no	—
136	C₅×C₂²⋊C₄	—	3	4	no	—
137	C₅×C₂²⋊C₄	—	6	4	no	—
138	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	6	2	no	—
141	C₂×H(5,𝔽₂)	—	3	1	no	—
142	#518	—	3	1	no	—
143	#518	C₅×D₃	1	1	yes	characteristic, complemented
144	#410	—	3	4	no	—
145	C₂×#99	—	3	8	no	—
146	C₂²×C₃×C₅	—	4	4	no	—
147	C₂²×C₃×C₅	—	4	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	4	1	no	—
150	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	8	yes	—
151	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₅×D₃	—	2	4	no	—
155	C₂×C₅×D₃	—	4	4	no	—
156	C₂×C₅×D₃	—	8	8	no	—
157	C₃×C₄×C₅	—	4	4	no	—
158	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
159	C₅×Dic₃	—	2	4	no	—
160	C₅×Dic₃	—	4	4	no	—
161	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
162	C₂³×D₃	C₂×C₄×C₅	1	4	yes	complemented
163	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
164	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
165	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
166	C₂²×C₃×C₄	—	2	4	no	—
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₂×#67	—	2	8	no	—
169	C₂×#67	—	2	8	no	—
170	C₂×#67	C₂×C₄×C₅	1	8	yes	complemented
171	C₂×#67	C₂³×C₅	1	4	yes	—
172	C₂²×Dic₃	—	2	4	no	—
173	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
174	#237	—	2	16	no	—
175	D₃×D₄	—	2	16	no	—
176	#235	—	2	4	no	—
177	#235	—	2	4	no	—
178	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	complemented
179	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
180	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	complemented
181	C₃×C₄⋊C₄	—	2	2	no	—
182	C₃×C₂²⋊C₄	—	2	4	no	—
183	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
184	C₃×C₄²	—	2	2	no	—
185	#217	—	2	4	no	—
186	#217	C₂³×C₅	1	4	yes	—
187	C₄⋊Dic₃	—	2	2	no	—
188	C₄×Dic₃	—	2	2	no	—
189	C₂³×C₅	—	3	4	no	—
190	C₂³×C₅	—	6	8	no	—
191	C₂³×C₅	—	8	2	no	—
192	C₂³×C₅	—	24	4	no	—
193	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
194	C₂³×C₅	C₂×D₁₂	1	4	yes	—
195	C₂³×C₅	C₂×#67	1	4	yes	—
196	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
197	C₅×Q₈	—	6	4	no	—
198	C₅×D₄	—	6	16	no	—
199	C₅×D₄	—	6	4	no	—
200	C₅×D₄	—	6	4	no	—
201	C₅×D₄	—	6	4	no	—
202	C₅×D₄	(C₂×D₃)⋊C₄	1	16	yes	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	3	4	no	—
205	C₂×C₄×C₅	—	6	8	no	—
206	C₂×C₄×C₅	—	6	8	no	—
207	C₂×C₄×C₅	—	6	4	no	—
208	C₂×C₄×C₅	—	8	4	no	—
209	C₂×C₄×C₅	—	24	4	no	—
210	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
211	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
212	C₂×C₄×C₅	C₂×#67	1	2	yes	—
213	H(5,𝔽₂)	—	6	4	no	—
214	H(5,𝔽₂)	—	6	4	no	—
215	C₂×#41	—	3	4	no	—
216	C₂×#41	—	3	2	no	—
217	C₂²×D₄	—	3	4	no	—
218	C₂²×D₄	—	3	4	no	—
219	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
220	C₄×D₄	—	2	4	no	—
221	C₄×D₄	—	6	4	no	—
222	#117	—	3	2	no	—
223	#117	C₂×C₅×D₃	1	2	yes	complemented
224	C₂×C₂²⋊C₄	—	3	4	no	—
225	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
226	#99	—	3	16	no	—
227	C₂×C₃×C₅	—	2	1	no	—
228	C₂×C₃×C₅	—	2	1	no	—
229	C₂×C₃×C₅	—	2	1	no	—
230	C₂×C₃×C₅	—	2	8	no	—
231	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₅×D₃	—	4	4	no	—
233	C₂³×C₃	—	8	2	no	—
234	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
235	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
236	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
237	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
238	C₂²×D₃	—	2	8	no	—
239	C₂²×D₃	—	8	4	no	—
240	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
241	C₃×D₄	C₅×C₂²⋊C₄	1	16	yes	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	8	4	no	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
245	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
246	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
247	#67	—	2	16	no	—
248	#67	—	2	4	no	—
249	#67	—	2	4	no	—
250	C₂×Dic₃	—	2	8	no	—
251	C₂×Dic₃	—	2	4	no	—
252	C₂×Dic₃	—	8	4	no	—
253	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
254	D₁₂	—	2	4	no	—
255	C₄×D₃	—	2	8	no	—
256	Dic₆	—	2	4	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	4	4	no	—
259	C₂²×C₅	—	4	1	no	—
260	C₂²×C₅	—	4	4	no	—
261	C₂²×C₅	—	6	4	no	—
262	C₂²×C₅	—	12	4	no	—
263	C₂²×C₅	—	24	8	no	—
264	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	8	yes	—
265	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
266	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
267	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
268	C₄×C₅	—	4	4	no	—
269	C₄×C₅	—	6	4	no	—
270	C₄×C₅	—	12	4	no	—
271	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
272	C₂⁴	—	3	4	no	—
273	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
274	#41	—	6	16	no	—
275	#41	—	6	4	no	—
276	#41	—	6	4	no	—
277	C₂×Q₈	—	3	2	no	—
278	C₂×D₄	—	3	8	no	—
279	C₂×D₄	—	3	4	no	—
280	C₂×D₄	—	3	2	no	—
281	C₂×D₄	—	6	8	no	—
282	C₂×D₄	—	6	8	no	—
283	C₂×D₄	—	6	16	no	—
284	C₂×D₄	C₄×C₅×D₃	1	4	yes	—
285	C₂×D₄	C₅×D₁₂	1	4	yes	—
286	C₂×D₄	C₅×#67	1	4	yes	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	3	4	no	—
289	C₂²×C₄	—	3	4	no	—
290	C₂²×C₄	—	6	4	no	—
291	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	6	2	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	3	4	no	—
296	C₂²⋊C₄	—	6	4	no	—
297	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
298	C₄²	—	2	2	no	—
299	C₄²	—	6	2	no	—
300	C₃×C₅	#2883	1	1	yes	characteristic, complemented, Hall
301	C₂²×C₃	—	4	4	no	—
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
306	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
307	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
308	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
309	C₂×D₃	—	2	4	no	—
310	C₂×D₃	—	4	4	no	—
311	C₂×D₃	—	8	8	no	—
312	C₃×C₄	—	4	4	no	—
313	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
314	Dic₃	—	2	4	no	—
315	Dic₃	—	4	4	no	—
316	C₂×C₅	—	2	1	no	—
317	C₂×C₅	—	2	1	no	—
318	C₂×C₅	—	2	1	no	—
319	C₂×C₅	—	2	8	no	—
320	C₂×C₅	—	12	4	no	—
321	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
322	C₂³	—	3	4	no	—
323	C₂³	—	6	8	no	—
324	C₂³	—	8	2	no	—
325	C₂³	—	24	4	no	—
326	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
327	C₂³	C₂×C₅×D₁₂	1	4	yes	—
328	C₂³	C₂×C₅×#67	1	4	yes	—
329	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
330	Q₈	—	6	4	no	—
331	D₄	—	6	16	no	—
332	D₄	—	6	4	no	—
333	D₄	—	6	4	no	—
334	D₄	—	6	4	no	—
335	D₄	C₅×(C₂×D₃)⋊C₄	1	16	yes	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	3	4	no	—
338	C₂×C₄	—	6	8	no	—
339	C₂×C₄	—	6	8	no	—
340	C₂×C₄	—	6	4	no	—
341	C₂×C₄	—	8	4	no	—
342	C₂×C₄	—	24	4	no	—
343	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
344	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
345	C₂×C₄	C₂×C₅×#67	1	2	yes	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	8	no	—
350	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
351	D₃	—	4	4	no	—
352	C₅	#82546	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	4	no	—
357	C₂²	—	6	4	no	—
358	C₂²	—	12	4	no	—
359	C₂²	—	24	8	no	—
360	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	8	yes	—
361	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
362	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
363	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
364	C₄	—	4	4	no	—
365	C₄	—	6	4	no	—
366	C₄	—	12	4	no	—
367	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
368	C₃	C₅×#2883	1	1	yes	characteristic, complemented, Sylow
369	C₂	—	2	1	no	—
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	2	8	no	—
373	C₂	—	12	4	no	—
374	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#518	C₂
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₅×#1004	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#518	D₃
hypocenter	C₃	C₅×#2883
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₅×D₄ ◁ C₅×#518

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#518	C₂	semidirect
3. C₅×#5798	C₂	semidirect
4. C₅×#5006	C₂	semidirect
5. C₂×C₅×#806	C₂	semidirect
11. C₂×C₅×#237	C₄	semidirect
12. C₂×C₅×D₃×D₄	C₄	semidirect
15. C₃×C₅×#117	C₂²	semidirect
16. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
17. C₂×C₅×#217	C₂²	semidirect
19. C₅×#926	C₂²	semidirect
20. C₅×#806	C₂²	semidirect
21. #82546	C₅	direct (N × H)
24. C₅×#518	D₃	semidirect
28. C₂³×C₅×D₃	C₂×C₄	semidirect
36. C₂×C₅×#67	C₂×C₄	semidirect
39. C₂²×C₅×Dic₃	C₂×C₄	semidirect
44. C₂×C₅×D₁₂	C₂×C₄	semidirect
45. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
46. C₂×C₅×Dic₆	C₂×C₄	semidirect
56. C₃×#518	C₂×C₅	semidirect
57. #5798	C₂×C₅	semidirect
58. #5006	C₂×C₅	semidirect
59. C₂×#806	C₂×C₅	semidirect
70. C₅×#117	C₂×D₃	semidirect
72. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
103. C₂×#237	C₄×C₅	semidirect
104. C₂×D₃×D₄	C₄×C₅	semidirect
107. C₃×#117	C₂²×C₅	semidirect
108. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
109. C₂×#217	C₂²×C₅	semidirect
111. #926	C₂²×C₅	semidirect
112. #806	C₂²×C₅	semidirect
143. #518	C₅×D₃	semidirect
162. C₂³×D₃	C₂×C₄×C₅	semidirect
170. C₂×#67	C₂×C₄×C₅	semidirect
173. C₂²×Dic₃	C₂×C₄×C₅	semidirect
178. C₂×D₁₂	C₂×C₄×C₅	semidirect
179. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
180. C₂×Dic₆	C₂×C₄×C₅	semidirect
223. #117	C₂×C₅×D₃	semidirect
225. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
300. C₃×C₅	#2883	semidirect
352. C₅	#82546	direct (N × H)
368. C₃	C₅×#2883	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1004	2
C₃×C₅×#518	2
C₅×#5798	2
C₅×#5006	2
C₂×C₅×#806	2
C₅×#2883	3
#82546	5

Subgroups — C5×#82546 #14411971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82546 #14411971