Subgroups — C₅×#68384 #14284839

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5716	C₂	1	1	yes	maximal, characteristic
2	C₅×#4837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1547	—	3	1	no	maximal, Hall
9	C₂×C₅×#237	—	2	1	no	—
10	C₃×C₅×#127	C₂²	1	1	yes	characteristic
11	C₅×#938	—	2	1	no	—
12	C₅×#938	C₄	1	2	yes	—
13	C₅×#936	—	2	1	no	—
14	C₅×D₄×Dic₃	—	2	1	no	—
15	C₅×D₄×Dic₃	C₄	1	2	yes	—
16	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
17	C₂×C₅×D₃×C₈	—	2	1	no	—
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₅×#869	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₅×Dic₃⋊C₈	—	2	1	no	—
23	C₅×Dic₃⋊C₈	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#68384	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#532	—	3	1	no	—
28	C₅×#423	—	3	1	no	—
29	C₂×C₅×C₄⋊C₈	—	3	1	no	—
30	C₅×#332	—	3	1	no	—
31	C₅×#332	—	3	1	no	—
32	C₅×#331	—	3	1	no	—
33	C₅×#331	D₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
37	C₂×C₅×#67	—	2	2	no	—
38	C₂²×C₅×Dic₃	—	2	2	no	—
39	C₅×#237	—	4	2	no	—
40	C₅×#237	—	4	2	no	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
44	C₂×C₅×Dic₆	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₅×#217	—	2	2	no	—
49	C₅×#217	—	2	2	no	—
50	C₅×C₄⋊Dic₃	—	2	1	no	—
51	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
52	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₅×ΓL(1,𝔽₂₅)	—	4	2	no	—
58	C₅×D₃×C₈	—	4	2	no	—
59	#5716	C₂×C₅	1	1	yes	characteristic
60	#4837	C₂×C₅	1	1	yes	characteristic, complemented
61	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#331	C₂×C₅	1	1	yes	characteristic, complemented
63	#4544	C₂×C₅	1	1	yes	characteristic, complemented
64	#4486	C₂×C₅	1	1	yes	characteristic, complemented
65	#4482	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	—	6	1	no	—
67	C₂×C₅×M₁₆	—	6	1	no	—
68	C₂²×C₅×C₈	—	6	1	no	—
69	C₅×C₄⋊Q₈	—	3	1	no	—
70	C₅×#127	C₂×D₃	1	1	yes	characteristic
71	C₅×#124	—	6	1	no	—
72	C₅×#121	—	3	2	no	—
73	C₅×#121	—	6	1	no	—
74	C₄×C₅×D₄	—	3	2	no	—
75	C₄×C₅×D₄	—	6	1	no	—
76	C₂×C₄²×C₅	—	3	1	no	—
77	C₅×C₄⋊C₈	—	3	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	—	6	1	no	—
80	C₅×C₄⋊C₈	—	6	1	no	—
81	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
82	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
83	#1547	—	3	1	no	Sylow
84	C₂³×C₃×C₅	—	2	2	no	—
85	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₃×C₅×D₄	—	4	2	no	—
87	C₃×C₅×D₄	—	4	1	no	—
88	C₃×C₅×D₄	—	4	1	no	—
89	C₃×C₅×D₄	—	4	1	no	—
90	C₃×C₅×D₄	—	4	1	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₅×#67	—	4	4	no	—
95	C₂×C₅×Dic₃	—	2	2	no	—
96	C₂×C₅×Dic₃	—	4	4	no	—
97	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄×C₅×D₃	—	2	1	no	—
101	C₄×C₅×D₃	—	2	1	no	—
102	C₄×C₅×D₃	—	4	1	no	—
103	C₄×C₅×D₃	D₈	1	2	yes	—
104	C₄×C₅×D₃	SD₁₆	1	2	yes	—
105	C₅×Dic₆	—	4	1	no	—
106	C₅×Dic₆	—	4	1	no	—
107	C₃×C₅×C₈	—	4	1	no	—
108	C₃×C₅×C₈	—	4	1	no	—
109	C₅×C₃⋊C₈	—	4	1	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₂×#237	—	2	1	no	—
112	C₃×#127	C₂²×C₅	1	1	yes	characteristic
113	#938	—	2	1	no	—
114	#938	C₄×C₅	1	2	yes	—
115	#936	—	2	1	no	—
116	D₄×Dic₃	—	2	1	no	—
117	D₄×Dic₃	C₄×C₅	1	2	yes	—
118	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
119	C₂×D₃×C₈	—	2	1	no	—
120	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
121	#869	C₂²×C₅	1	1	yes	characteristic
122	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
123	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	Dic₃⋊C₈	—	2	1	no	—
125	Dic₃⋊C₈	—	2	1	no	—
126	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
127	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
128	C₅×#41	—	12	2	no	—
129	C₅×#41	—	12	2	no	—
130	C₂×C₅×Q₈	—	6	1	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	6	2	no	—
134	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
135	C₂²×C₄×C₅	—	3	1	no	—
136	C₂²×C₄×C₅	—	3	1	no	—
137	C₂²×C₄×C₅	—	3	1	no	—
138	C₂²×C₄×C₅	—	6	2	no	—
139	C₅×M₁₆	—	12	2	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	6	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₂×C₅×C₈	—	12	2	no	—
145	C₅×C₄⋊C₄	—	3	2	no	—
146	C₅×C₄⋊C₄	—	6	1	no	—
147	C₅×C₂²⋊C₄	—	6	2	no	—
148	C₅×C₂²⋊C₄	—	6	2	no	—
149	C₄²×C₅	—	3	1	no	—
150	C₄²×C₅	—	3	1	no	—
151	C₄²×C₅	—	3	1	no	—
152	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
153	#532	—	3	1	no	—
154	#423	—	3	1	no	—
155	C₂×C₄⋊C₈	—	3	1	no	—
156	#332	—	3	1	no	—
157	#332	—	3	1	no	—
158	#331	—	3	1	no	—
159	#331	C₅×D₃	1	1	yes	characteristic, complemented
160	C₂²×C₃×C₅	—	4	2	no	—
161	C₂²×C₃×C₅	—	4	2	no	—
162	C₂²×C₃×C₅	—	4	2	no	—
163	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₅×D₃	—	2	1	no	—
165	C₂×C₅×D₃	—	2	1	no	—
166	C₂×C₅×D₃	#102	1	2	yes	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
170	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₃×C₄×C₅	#137	1	1	yes	characteristic
172	C₅×Dic₃	—	2	1	no	—
173	C₅×Dic₃	—	2	1	no	—
174	C₅×Dic₃	—	4	2	no	—
175	C₅×Dic₃	#102	1	2	yes	—
176	C₂×C₃×D₄	—	2	1	no	—
177	C₂×C₃×D₄	—	2	1	no	—
178	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
179	C₂×#67	—	2	2	no	—
180	C₂²×Dic₃	—	2	2	no	—
181	#237	—	4	2	no	—
182	#237	—	4	2	no	—
183	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
184	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
185	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
186	C₂×Dic₆	—	2	1	no	—
187	C₂×C₃×C₈	—	2	1	no	—
188	C₂×C₃×C₈	—	2	1	no	—
189	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
190	#217	—	2	2	no	—
191	#217	—	2	2	no	—
192	C₄⋊Dic₃	—	2	1	no	—
193	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
194	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
195	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
196	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
197	C₂×C₃⋊C₈	—	2	1	no	—
198	C₂×C₃⋊C₈	—	2	1	no	—
199	ΓL(1,𝔽₂₅)	—	4	2	no	—
200	D₃×C₈	—	4	2	no	—
201	C₂³×C₅	—	2	2	no	—
202	C₂³×C₅	—	3	1	no	—
203	C₅×Q₈	—	12	1	no	—
204	C₅×Q₈	—	12	1	no	—
205	C₅×D₄	—	4	2	no	—
206	C₅×D₄	—	4	1	no	—
207	C₅×D₄	—	4	1	no	—
208	C₅×D₄	—	4	1	no	—
209	C₅×D₄	—	4	1	no	—
210	C₅×D₄	—	12	4	no	—
211	C₂×C₄×C₅	—	3	1	no	—
212	C₂×C₄×C₅	—	3	2	no	—
213	C₂×C₄×C₅	—	3	2	no	—
214	C₂×C₄×C₅	—	3	1	no	—
215	C₂×C₄×C₅	—	3	1	no	—
216	C₂×C₄×C₅	—	6	1	no	—
217	C₂×C₄×C₅	—	6	1	no	—
218	C₂×C₄×C₅	—	6	2	no	—
219	C₂×C₄×C₅	—	12	1	no	—
220	C₂×C₄×C₅	—	12	4	no	—
221	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
222	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
224	C₅×C₈	—	4	1	no	—
225	C₅×C₈	—	4	1	no	—
226	C₅×C₈	—	12	1	no	—
227	C₅×C₈	—	12	1	no	—
228	C₂×#41	—	6	1	no	—
229	C₂×M₁₆	—	6	1	no	—
230	C₂²×C₈	—	6	1	no	—
231	C₄⋊Q₈	—	3	1	no	—
232	#127	C₂×C₅×D₃	1	1	yes	characteristic
233	#124	—	6	1	no	—
234	#121	—	3	2	no	—
235	#121	—	6	1	no	—
236	C₄×D₄	—	3	2	no	—
237	C₄×D₄	—	6	1	no	—
238	C₂×C₄²	—	3	1	no	—
239	C₄⋊C₈	—	3	1	no	—
240	C₄⋊C₈	—	3	1	no	—
241	C₄⋊C₈	—	6	1	no	—
242	C₄⋊C₈	—	6	1	no	—
243	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
244	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
245	C₂×C₃×C₅	—	8	2	no	—
246	C₂×C₃×C₅	#413	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
248	C₂×C₃×C₅	#417	1	1	yes	characteristic
249	C₅×D₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
252	C₃×D₄	—	4	2	no	—
253	C₃×D₄	—	4	1	no	—
254	C₃×D₄	—	4	1	no	—
255	C₃×D₄	—	4	1	no	—
256	C₃×D₄	—	4	1	no	—
257	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	#67	—	4	4	no	—
261	C₂×Dic₃	—	2	2	no	—
262	C₂×Dic₃	—	4	4	no	—
263	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₄×D₃	—	2	1	no	—
267	C₄×D₃	—	2	1	no	—
268	C₄×D₃	—	4	1	no	—
269	C₄×D₃	C₅×D₈	1	2	yes	—
270	C₄×D₃	C₅×SD₁₆	1	2	yes	—
271	Dic₆	—	4	1	no	—
272	Dic₆	—	4	1	no	—
273	C₃×C₈	—	4	1	no	—
274	C₃×C₈	—	4	1	no	—
275	C₃⋊C₈	—	4	1	no	—
276	C₃⋊C₈	—	4	1	no	—
277	C₂²×C₅	—	3	2	no	—
278	C₂²×C₅	—	4	2	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	6	1	no	—
282	C₂²×C₅	—	6	1	no	—
283	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	3	2	no	—
286	C₄×C₅	—	6	1	no	—
287	C₄×C₅	—	6	1	no	—
288	C₄×C₅	—	12	2	no	—
289	C₄×C₅	D₃×D₈	1	1	yes	characteristic
290	C₄×C₅	#911	1	1	yes	characteristic
291	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
292	C₄×C₅	#915	1	1	yes	characteristic
293	#41	—	12	2	no	—
294	#41	—	12	2	no	—
295	C₂×Q₈	—	6	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	6	2	no	—
299	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
300	C₂²×C₄	—	3	1	no	—
301	C₂²×C₄	—	3	1	no	—
302	C₂²×C₄	—	3	1	no	—
303	C₂²×C₄	—	6	2	no	—
304	M₁₆	—	12	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	6	1	no	—
308	C₂×C₈	—	6	1	no	—
309	C₂×C₈	—	12	2	no	—
310	C₄⋊C₄	—	3	2	no	—
311	C₄⋊C₄	—	6	1	no	—
312	C₂²⋊C₄	—	6	2	no	—
313	C₂²⋊C₄	—	6	2	no	—
314	C₄²	—	3	1	no	—
315	C₄²	—	3	1	no	—
316	C₄²	—	3	1	no	—
317	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
318	C₃×C₅	#1547	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×D₃	—	2	1	no	—
324	C₂×D₃	—	2	1	no	—
325	C₂×D₃	C₅×#102	1	2	yes	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
328	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
329	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
330	C₃×C₄	C₅×#137	1	1	yes	characteristic
331	Dic₃	—	2	1	no	—
332	Dic₃	—	2	1	no	—
333	Dic₃	—	4	2	no	—
334	Dic₃	C₅×#102	1	2	yes	—
335	C₂×C₅	—	6	2	no	—
336	C₂×C₅	—	8	2	no	—
337	C₂×C₅	#4745	1	1	yes	characteristic
338	C₂×C₅	D₃×#102	1	1	yes	characteristic
339	C₂×C₅	#4771	1	1	yes	characteristic
340	C₂³	—	2	2	no	—
341	C₂³	—	3	1	no	—
342	Q₈	—	12	1	no	—
343	Q₈	—	12	1	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	1	no	—
346	D₄	—	4	1	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	12	4	no	—
350	C₂×C₄	—	3	1	no	—
351	C₂×C₄	—	3	2	no	—
352	C₂×C₄	—	3	2	no	—
353	C₂×C₄	—	3	1	no	—
354	C₂×C₄	—	3	1	no	—
355	C₂×C₄	—	6	1	no	—
356	C₂×C₄	—	6	1	no	—
357	C₂×C₄	—	6	2	no	—
358	C₂×C₄	—	12	1	no	—
359	C₂×C₄	—	12	4	no	—
360	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
361	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
362	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
363	C₈	—	4	1	no	—
364	C₈	—	4	1	no	—
365	C₈	—	12	1	no	—
366	C₈	—	12	1	no	—
367	C₂×C₃	—	8	2	no	—
368	C₂×C₃	C₅×#413	1	1	yes	characteristic
369	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
370	C₂×C₃	C₅×#417	1	1	yes	characteristic
371	D₃	—	2	2	no	—
372	C₅	#68384	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	3	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	6	1	no	—
378	C₂²	—	6	1	no	—
379	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	3	2	no	—
382	C₄	—	6	1	no	—
383	C₄	—	6	1	no	—
384	C₄	—	12	2	no	—
385	C₄	C₅×D₃×D₈	1	1	yes	characteristic
386	C₄	C₅×#911	1	1	yes	characteristic
387	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
388	C₄	C₅×#915	1	1	yes	characteristic
389	C₃	C₅×#1547	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	6	2	no	—
391	C₂	—	8	2	no	—
392	C₂	C₅×#4745	1	1	yes	characteristic
393	C₂	C₅×D₃×#102	1	1	yes	characteristic
394	C₂	C₅×#4771	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#331	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5716	C₂
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#331	D₃
hypocenter	C₃	C₅×#1547
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#331

Complements

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

N	H ≅ G/N	type
2. C₅×#4837	C₂	semidirect
3. C₅×D₃×C₄⋊C₈	C₂	semidirect
4. C₃×C₅×#331	C₂	semidirect
5. C₅×#4544	C₂	semidirect
6. C₅×#4486	C₂	semidirect
7. C₅×#4482	C₂	semidirect
26. #68384	C₅	direct (N × H)
33. C₅×#331	D₃	semidirect
60. #4837	C₂×C₅	semidirect
61. D₃×C₄⋊C₈	C₂×C₅	semidirect
62. C₃×#331	C₂×C₅	semidirect
63. #4544	C₂×C₅	semidirect
64. #4486	C₂×C₅	semidirect
65. #4482	C₂×C₅	semidirect
159. #331	C₅×D₃	semidirect
318. C₃×C₅	#1547	semidirect
372. C₅	#68384	direct (N × H)
389. C₃	C₅×#1547	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5716	2
C₅×#4837	2
C₅×D₃×C₄⋊C₈	2
C₃×C₅×#331	2
C₅×#4544	2
C₅×#4486	2
C₅×#4482	2
C₅×#1547	3
#68384	5

Subgroups — C5×#68384 #14284839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68384 #14284839