Subgroups — C₅×#78579 #14418023

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5748	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#901	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5125	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5005	C₂	1	2	yes	maximal, complemented
6	C₅×#4717	C₂	1	4	yes	maximal, complemented
7	C₅×#4700	C₂	1	4	yes	maximal, complemented
8	C₅×#2955	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	2	yes	—
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	2	yes	—
14	C₅×#909	C₄	1	4	yes	complemented
15	C₅×#908	C₄	1	4	yes	complemented
16	C₅×#904	C₂²	1	4	yes	—
17	C₅×#901	—	2	2	no	—
18	C₅×#901	—	2	2	no	—
19	C₅×#901	C₂²	1	4	yes	complemented
20	C₅×#901	C₂²	1	4	yes	complemented
21	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
22	C₂×C₅×D₃×C₈	—	2	2	no	—
23	C₃×C₅×#97	C₂²	1	2	yes	complemented
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
25	C₅×#819	C₂²	1	4	yes	complemented
26	C₅×#805	C₂²	1	8	yes	complemented
27	#78579	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₅×#575	—	3	1	no	—
29	C₂×C₅×#131	—	3	2	no	—
30	C₅×#444	—	3	4	no	—
31	C₅×#443	—	3	4	no	—
32	C₅×#430	—	3	1	no	—
33	C₅×#421	—	3	2	no	—
34	C₅×#405	D₃	1	1	yes	characteristic, complemented
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₅×#67	—	2	2	no	—
37	C₅×#235	—	2	2	no	—
38	C₅×#235	—	2	2	no	—
39	C₅×#235	C₂×C₄	1	4	yes	—
40	C₅×#235	C₂³	1	4	yes	—
41	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
42	C₂×C₄×C₅×D₃	—	2	2	no	—
43	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
44	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
45	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	2	yes	—
53	C₅×#208	—	2	2	no	—
54	C₅×#208	C₂³	1	4	yes	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₅×Dic₁₂	C₂×C₄	1	4	yes	—
57	C₅×D₂₄	C₂×C₄	1	4	yes	—
58	C₅×#204	C₂×C₄	1	8	yes	—
59	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
60	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
61	C₅×D₃×C₈	—	2	4	no	—
62	C₅×D₃×C₈	—	2	4	no	—
63	#5748	C₂×C₅	1	1	yes	characteristic
64	C₂×#901	C₂×C₅	1	2	yes	complemented
65	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
66	#5125	C₂×C₅	1	1	yes	characteristic, complemented
67	#5005	C₂×C₅	1	2	yes	complemented
68	#4717	C₂×C₅	1	4	yes	complemented
69	#4700	C₂×C₅	1	4	yes	complemented
70	C₂×C₅×#41	—	3	2	no	—
71	C₅×#137	—	3	4	no	—
72	C₅×AGL(1,ℤ/8)	—	3	4	no	—
73	C₅×#135	—	3	4	no	—
74	C₅×#131	—	3	4	no	—
75	C₅×#131	—	3	4	no	—
76	C₅×#131	—	6	2	no	—
77	C₅×#131	—	6	2	no	—
78	C₂×C₅×M₁₆	—	3	2	no	—
79	C₂×C₅×M₁₆	—	6	2	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	6	2	no	—
82	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
83	C₅×#117	C₂×D₃	1	1	yes	characteristic
84	C₅×#108	—	3	4	no	—
85	C₅×#104	—	3	8	no	—
86	C₅×#97	C₂×D₃	1	2	yes	complemented
87	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
88	#2955	—	3	1	no	Sylow
89	C₂³×C₃×C₅	#41	1	1	yes	characteristic
90	C₂²×C₅×D₃	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₅×#67	—	2	4	no	—
97	C₅×#67	—	2	4	no	—
98	C₂×C₅×Dic₃	—	2	2	no	—
99	C₅×D₁₂	—	2	2	no	—
100	C₅×D₁₂	C₂²×C₄	1	4	yes	—
101	C₄×C₅×D₃	—	2	4	no	—
102	C₄×C₅×D₃	—	2	4	no	—
103	C₅×Dic₆	—	2	2	no	—
104	C₅×Dic₆	C₂²×C₄	1	4	yes	—
105	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
106	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
107	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
108	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
109	C₅×C₃⋊C₈	—	2	4	no	—
110	C₂×#235	C₂²×C₅	1	2	yes	—
111	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
112	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
113	C₃×#117	C₂²×C₅	1	1	yes	characteristic
114	C₂×#208	C₂²×C₅	1	2	yes	—
115	#909	C₄×C₅	1	4	yes	complemented
116	#908	C₄×C₅	1	4	yes	complemented
117	#904	C₂²×C₅	1	4	yes	—
118	#901	—	2	2	no	—
119	#901	—	2	2	no	—
120	#901	C₂²×C₅	1	4	yes	complemented
121	#901	C₂²×C₅	1	4	yes	complemented
122	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
123	C₂×D₃×C₈	—	2	2	no	—
124	C₃×#97	C₂²×C₅	1	2	yes	complemented
125	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
126	#819	C₂²×C₅	1	4	yes	complemented
127	#805	C₂²×C₅	1	8	yes	complemented
128	C₅×#41	—	3	4	no	—
129	C₅×#41	—	3	4	no	—
130	C₅×#41	—	6	2	no	—
131	C₅×#41	—	6	2	no	—
132	C₂×C₅×Q₈	—	3	2	no	—
133	C₂×C₅×D₄	—	3	2	no	—
134	C₂×C₅×D₄	—	6	2	no	—
135	C₂²×C₄×C₅	—	6	2	no	—
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₅×Q₁₆	—	3	4	no	—
138	C₅×SD₁₆	—	3	8	no	—
139	C₅×D₈	—	3	4	no	—
140	C₅×M₁₆	—	3	4	no	—
141	C₅×M₁₆	—	6	2	no	—
142	C₅×M₁₆	—	6	4	no	—
143	C₅×M₁₆	—	6	4	no	—
144	C₅×M₁₆	C₄×D₃	1	4	yes	—
145	C₂×C₅×C₈	—	6	2	no	—
146	C₂×C₅×C₈	—	6	4	no	—
147	C₂×C₅×C₈	—	6	4	no	—
148	C₂×C₅×C₈	D₁₂	1	2	yes	—
149	C₂×C₅×C₈	D₁₂	1	2	yes	—
150	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
151	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₄²×C₅	C₂²×D₃	1	2	yes	—
156	#575	—	3	1	no	—
157	C₂×#131	—	3	2	no	—
158	#444	—	3	4	no	—
159	#443	—	3	4	no	—
160	#430	—	3	1	no	—
161	#421	—	3	2	no	—
162	#405	C₅×D₃	1	1	yes	characteristic, complemented
163	C₂²×C₃×C₅	—	4	1	no	—
164	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
165	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
166	C₂×C₅×D₃	—	2	4	no	—
167	C₂×C₅×D₃	—	4	4	no	—
168	C₃×C₄×C₅	—	4	2	no	—
169	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
170	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₅×Dic₃	—	2	4	no	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂×#67	—	2	2	no	—
175	#235	—	2	2	no	—
176	#235	—	2	2	no	—
177	#235	C₂×C₄×C₅	1	4	yes	—
178	#235	C₂³×C₅	1	4	yes	—
179	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
180	C₂×C₄×D₃	—	2	2	no	—
181	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
182	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	—
183	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
184	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
185	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
186	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
187	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₂²⋊C₄	—	2	1	no	—
190	C₃×C₄²	C₂³×C₅	1	2	yes	—
191	#208	—	2	2	no	—
192	#208	C₂³×C₅	1	4	yes	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	Dic₁₂	C₂×C₄×C₅	1	4	yes	—
195	D₂₄	C₂×C₄×C₅	1	4	yes	—
196	#204	C₂×C₄×C₅	1	8	yes	—
197	ΓL(1,𝔽₂₅)	—	2	4	no	—
198	ΓL(1,𝔽₂₅)	—	2	4	no	—
199	D₃×C₈	—	2	4	no	—
200	D₃×C₈	—	2	4	no	—
201	C₂³×C₅	—	6	2	no	—
202	C₂³×C₅	#235	1	1	yes	characteristic
203	C₅×Q₈	—	3	4	no	—
204	C₅×Q₈	—	6	2	no	—
205	C₅×D₄	—	3	4	no	—
206	C₅×D₄	—	6	4	no	—
207	C₅×D₄	—	6	4	no	—
208	C₅×D₄	—	6	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	6	2	no	—
211	C₂×C₄×C₅	—	6	4	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
214	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
215	C₂×C₄×C₅	#235	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
217	C₅×C₈	—	6	4	no	—
218	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
219	C₅×C₈	C₂×D₁₂	1	2	yes	—
220	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
221	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
222	C₂×#41	—	3	2	no	—
223	#137	—	3	4	no	—
224	AGL(1,ℤ/8)	—	3	4	no	—
225	#135	—	3	4	no	—
226	#131	—	3	4	no	—
227	#131	—	3	4	no	—
228	#131	—	6	2	no	—
229	#131	—	6	2	no	—
230	C₂×M₁₆	—	3	2	no	—
231	C₂×M₁₆	—	6	2	no	—
232	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
233	C₂²×C₈	—	6	2	no	—
234	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
235	#117	C₂×C₅×D₃	1	1	yes	characteristic
236	#108	—	3	4	no	—
237	#104	—	3	8	no	—
238	#97	C₂×C₅×D₃	1	2	yes	complemented
239	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	2	2	no	—
242	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
243	C₅×D₃	—	4	4	no	—
244	C₂³×C₃	C₅×#41	1	1	yes	characteristic
245	C₂²×D₃	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
248	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
249	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
251	#67	—	2	4	no	—
252	#67	—	2	4	no	—
253	C₂×Dic₃	—	2	2	no	—
254	D₁₂	—	2	2	no	—
255	D₁₂	C₂²×C₄×C₅	1	4	yes	—
256	C₄×D₃	—	2	4	no	—
257	C₄×D₃	—	2	4	no	—
258	Dic₆	—	2	2	no	—
259	Dic₆	C₂²×C₄×C₅	1	4	yes	—
260	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
261	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
262	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
263	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
264	C₃⋊C₈	—	2	4	no	—
265	C₂²×C₅	—	4	1	no	—
266	C₂²×C₅	—	6	4	no	—
267	C₂²×C₅	—	12	4	no	—
268	C₂²×C₅	C₄×D₁₂	1	2	yes	—
269	C₂²×C₅	C₂×#235	1	1	yes	characteristic
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	—	6	4	no	—
272	C₄×C₅	C₄×D₁₂	1	2	yes	—
273	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
274	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
275	#41	—	3	4	no	—
276	#41	—	3	4	no	—
277	#41	—	6	2	no	—
278	#41	—	6	2	no	—
279	C₂×Q₈	—	3	2	no	—
280	C₂×D₄	—	3	2	no	—
281	C₂×D₄	—	6	2	no	—
282	C₂²×C₄	—	6	2	no	—
283	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
284	Q₁₆	—	3	4	no	—
285	SD₁₆	—	3	8	no	—
286	D₈	—	3	4	no	—
287	M₁₆	—	3	4	no	—
288	M₁₆	—	6	2	no	—
289	M₁₆	—	6	4	no	—
290	M₁₆	—	6	4	no	—
291	M₁₆	C₄×C₅×D₃	1	4	yes	—
292	C₂×C₈	—	6	2	no	—
293	C₂×C₈	—	6	4	no	—
294	C₂×C₈	—	6	4	no	—
295	C₂×C₈	C₅×D₁₂	1	2	yes	—
296	C₂×C₈	C₅×D₁₂	1	2	yes	—
297	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
298	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
299	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
300	C₄⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₄²	C₂²×C₅×D₃	1	2	yes	—
303	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
306	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
307	C₂×D₃	—	2	4	no	—
308	C₂×D₃	—	4	4	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
311	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
312	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
313	Dic₃	—	2	4	no	—
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	12	4	no	—
317	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
318	C₂³	—	6	2	no	—
319	C₂³	C₅×#235	1	1	yes	characteristic
320	Q₈	—	3	4	no	—
321	Q₈	—	6	2	no	—
322	D₄	—	3	4	no	—
323	D₄	—	6	4	no	—
324	D₄	—	6	4	no	—
325	D₄	—	6	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	6	2	no	—
328	C₂×C₄	—	6	4	no	—
329	C₂×C₄	—	6	4	no	—
330	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
331	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
332	C₂×C₄	C₅×#235	1	1	yes	characteristic
333	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
334	C₈	—	6	4	no	—
335	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
336	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
337	C₈	C₂×C₅×D₁₂	1	2	yes	—
338	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
342	D₃	—	4	4	no	—
343	C₅	#78579	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²	—	4	1	no	—
345	C₂²	—	6	4	no	—
346	C₂²	—	12	4	no	—
347	C₂²	C₄×C₅×D₁₂	1	2	yes	—
348	C₂²	C₂×C₅×#235	1	1	yes	characteristic
349	C₄	—	4	2	no	—
350	C₄	—	6	4	no	—
351	C₄	C₄×C₅×D₁₂	1	2	yes	—
352	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
353	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
354	C₃	C₅×#2955	1	1	yes	characteristic, complemented, Sylow
355	C₂	—	2	1	no	—
356	C₂	—	2	2	no	—
357	C₂	—	12	4	no	—
358	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₈	C₂×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₅×#5748	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#2955
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₂²×C₅×C₈ ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#901	C₂	semidirect
3. C₃×C₅×#405	C₂	semidirect
4. C₅×#5125	C₂	semidirect
5. C₅×#5005	C₂	semidirect
6. C₅×#4717	C₂	semidirect
7. C₅×#4700	C₂	semidirect
14. C₅×#909	C₄	semidirect
15. C₅×#908	C₄	semidirect
19. C₅×#901	C₂²	semidirect
20. C₅×#901	C₂²	semidirect
23. C₃×C₅×#97	C₂²	semidirect
24. C₃×C₄×C₅×C₈	C₂²	semidirect
25. C₅×#819	C₂²	semidirect
26. C₅×#805	C₂²	semidirect
27. #78579	C₅	direct (N × H)
34. C₅×#405	D₃	semidirect
64. C₂×#901	C₂×C₅	semidirect
65. C₃×#405	C₂×C₅	semidirect
66. #5125	C₂×C₅	semidirect
67. #5005	C₂×C₅	semidirect
68. #4717	C₂×C₅	semidirect
69. #4700	C₂×C₅	semidirect
86. C₅×#97	C₂×D₃	semidirect
87. C₄×C₅×C₈	C₂×D₃	semidirect
115. #909	C₄×C₅	semidirect
116. #908	C₄×C₅	semidirect
120. #901	C₂²×C₅	semidirect
121. #901	C₂²×C₅	semidirect
124. C₃×#97	C₂²×C₅	semidirect
125. C₃×C₄×C₈	C₂²×C₅	semidirect
126. #819	C₂²×C₅	semidirect
127. #805	C₂²×C₅	semidirect
162. #405	C₅×D₃	semidirect
238. #97	C₂×C₅×D₃	semidirect
239. C₄×C₈	C₂×C₅×D₃	semidirect
303. C₃×C₅	#2955	semidirect
343. C₅	#78579	direct (N × H)
354. C₃	C₅×#2955	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5748	2
C₂×C₅×#901	2
C₃×C₅×#405	2
C₅×#5125	2
C₅×#5005	2
C₅×#4717	2
C₅×#4700	2
C₅×#2955	3
#78579	5

Subgroups — C5×#78579 #14418023

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78579 #14418023