Subgroups — C₅×#81760 #14438880

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#916	C₂	1	4	yes	maximal, complemented
2	C₅×#5725	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5716	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5168	C₂	1	4	yes	maximal, complemented
6	C₅×#5092	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5073	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4693	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3147	—	3	1	no	maximal, Hall
11	C₂×C₅×#239	C₂²	1	2	yes	—
12	C₂×C₅×#237	C₂²	1	2	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₅×#947	C₂²	1	2	yes	—
17	C₂×C₅×#216	C₂²	1	4	yes	—
18	C₅×#938	—	2	2	no	—
19	C₅×#936	C₂²	1	2	yes	—
20	C₅×D₄×Dic₃	—	2	2	no	—
21	C₂×C₅×#213	C₂²	1	4	yes	—
22	C₅×#916	—	2	16	no	—
23	C₂×C₅×#204	C₂²	1	4	yes	—
24	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
25	C₅×#895	—	2	2	no	—
26	C₅×#893	—	2	2	no	—
27	C₅×#874	C₂²	1	1	yes	characteristic
28	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₅×#869	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₅×C₈×Dic₃	C₂²	1	2	yes	—
32	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	#81760	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#135	—	3	4	no	—
35	C₅×#532	—	3	1	no	—
36	C₅×#532	—	3	1	no	—
37	C₅×#495	—	3	4	no	—
38	C₅×#494	—	3	1	no	—
39	C₅×#493	—	3	1	no	—
40	C₅×#492	—	3	1	no	—
41	C₅×#492	D₃	1	1	yes	characteristic, complemented
42	C₂×C₄×C₅×C₈	—	3	1	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂×C₅×#67	—	2	2	no	—
47	C₂²×C₅×Dic₃	—	2	2	no	—
48	C₅×#239	—	2	8	no	—
49	C₅×#237	—	2	8	no	—
50	C₂×C₅×D₁₂	—	2	2	no	—
51	C₂×C₅×D₁₂	—	2	2	no	—
52	C₂×C₅×D₁₂	C₂³	1	2	yes	—
53	C₂×C₄×C₅×D₃	—	2	2	no	—
54	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
55	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
56	C₂×C₅×Dic₆	C₂³	1	2	yes	—
57	C₃×C₅×SD₁₆	—	2	8	no	—
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₅×#217	—	2	4	no	—
62	C₅×#216	—	2	8	no	—
63	C₅×#213	—	2	8	no	—
64	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
65	C₅×C₄⋊Dic₃	—	2	2	no	—
66	C₄×C₅×Dic₃	D₄	1	2	yes	—
67	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
69	C₅×#204	—	2	8	no	—
70	C₅×D₃×C₈	D₄	1	8	yes	complemented
71	C₂×#916	C₂×C₅	1	4	yes	complemented
72	#5725	C₂×C₅	1	1	yes	characteristic, complemented
73	#5716	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
75	#5168	C₂×C₅	1	4	yes	complemented
76	#5092	C₂×C₅	1	1	yes	characteristic, complemented
77	#5073	C₂×C₅	1	1	yes	characteristic, complemented
78	#4693	C₂×C₅	1	1	yes	characteristic, complemented
79	C₄×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×C₅×#41	—	3	2	no	—
81	C₂×C₅×#41	—	3	2	no	—
82	C₅×#135	—	6	16	no	—
83	C₂×C₅×Q₁₆	—	3	4	no	—
84	C₂×C₅×SD₁₆	—	3	4	no	—
85	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	—
86	C₂×C₅×D₈	—	3	4	no	—
87	C₂²×C₅×C₈	—	3	2	no	—
88	C₅×C₄⋊Q₈	—	3	1	no	—
89	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
90	C₅×#127	—	3	1	no	—
91	C₅×#127	C₂×D₃	1	1	yes	characteristic
92	C₅×#124	—	3	2	no	—
93	C₅×#124	—	3	2	no	—
94	C₅×#121	—	6	2	no	—
95	C₅×#121	—	6	2	no	—
96	C₄×C₅×D₄	—	6	2	no	—
97	C₄×C₅×D₄	—	6	2	no	—
98	C₂×C₄²×C₅	—	3	1	no	—
99	C₄×C₅×C₈	—	3	2	no	—
100	C₄×C₅×C₈	—	3	1	no	—
101	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	#3147	—	3	1	no	Sylow
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×D₄	—	2	4	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₅×#67	—	4	4	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	4	4	no	—
115	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
116	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
117	C₅×D₁₂	—	2	4	no	—
118	C₅×D₁₂	—	4	4	no	—
119	C₅×D₁₂	—	4	4	no	—
120	C₄×C₅×D₃	—	2	4	no	—
121	C₄×C₅×D₃	—	4	4	no	—
122	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
123	C₅×Dic₆	—	2	4	no	—
124	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
125	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
126	C₂×#239	C₂²×C₅	1	2	yes	—
127	C₂×#237	C₂²×C₅	1	2	yes	—
128	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
129	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₃×#127	C₂²×C₅	1	1	yes	characteristic
131	#947	C₂²×C₅	1	2	yes	—
132	C₂×#216	C₂²×C₅	1	4	yes	—
133	#938	—	2	2	no	—
134	#936	C₂²×C₅	1	2	yes	—
135	D₄×Dic₃	—	2	2	no	—
136	C₂×#213	C₂²×C₅	1	4	yes	—
137	#916	—	2	16	no	—
138	C₂×#204	C₂²×C₅	1	4	yes	—
139	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
140	#895	—	2	2	no	—
141	#893	—	2	2	no	—
142	#874	C₂²×C₅	1	1	yes	characteristic
143	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
144	#869	C₂²×C₅	1	1	yes	characteristic
145	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
146	C₈×Dic₃	C₂²×C₅	1	2	yes	—
147	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
148	C₅×#41	—	6	8	no	—
149	C₅×#41	—	6	8	no	—
150	C₂×C₅×Q₈	—	3	2	no	—
151	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	3	2	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂×C₅×D₄	—	6	2	no	—
156	C₂×C₅×D₄	—	6	2	no	—
157	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
158	C₂²×C₄×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	3	2	no	—
160	C₂²×C₄×C₅	—	6	2	no	—
161	C₂²×C₄×C₅	—	6	2	no	—
162	C₅×Q₁₆	—	6	8	no	—
163	C₅×SD₁₆	—	2	8	no	—
164	C₅×SD₁₆	—	6	8	no	—
165	C₅×D₈	—	6	8	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₂×C₅×C₈	—	3	8	no	—
168	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	6	2	no	—
171	C₅×C₂²⋊C₄	—	6	4	no	—
172	C₅×C₂²⋊C₄	—	6	4	no	—
173	C₄²×C₅	—	3	2	no	—
174	C₄²×C₅	—	3	1	no	—
175	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
176	C₂×#135	—	3	4	no	—
177	#532	—	3	1	no	—
178	#532	—	3	1	no	—
179	#495	—	3	4	no	—
180	#494	—	3	1	no	—
181	#493	—	3	1	no	—
182	#492	—	3	1	no	—
183	#492	C₅×D₃	1	1	yes	characteristic, complemented
184	C₂×C₄×C₈	—	3	1	no	—
185	C₂²×C₃×C₅	—	4	2	no	—
186	C₂²×C₃×C₅	—	4	4	no	—
187	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₅×D₃	—	2	2	no	—
189	C₂×C₅×D₃	—	4	2	no	—
190	C₂×C₅×D₃	—	4	4	no	—
191	C₂×C₅×D₃	#127	1	2	yes	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	#135	1	4	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
195	C₅×Dic₃	—	2	2	no	—
196	C₅×Dic₃	—	4	2	no	—
197	C₅×Dic₃	#127	1	2	yes	—
198	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
199	C₂×C₃×D₄	—	2	2	no	—
200	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
201	C₂×#67	—	2	2	no	—
202	C₂²×Dic₃	—	2	2	no	—
203	#239	—	2	8	no	—
204	#237	—	2	8	no	—
205	C₂×D₁₂	—	2	2	no	—
206	C₂×D₁₂	—	2	2	no	—
207	C₂×D₁₂	C₂³×C₅	1	2	yes	—
208	C₂×C₄×D₃	—	2	2	no	—
209	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
210	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
211	C₂×Dic₆	C₂³×C₅	1	2	yes	—
212	C₃×SD₁₆	—	2	8	no	—
213	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	2	2	no	—
215	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
216	#217	—	2	4	no	—
217	#216	—	2	8	no	—
218	#213	—	2	8	no	—
219	(C₂×D₃)⋊C₄	—	2	4	no	—
220	C₄⋊Dic₃	—	2	2	no	—
221	C₄×Dic₃	C₅×D₄	1	2	yes	—
222	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
223	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
224	#204	—	2	8	no	—
225	D₃×C₈	C₅×D₄	1	8	yes	complemented
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	3	1	no	—
228	C₂³×C₅	—	6	2	no	—
229	C₅×Q₈	—	2	4	no	—
230	C₅×Q₈	—	6	4	no	—
231	C₅×D₄	—	2	4	no	—
232	C₅×D₄	—	4	4	no	—
233	C₅×D₄	—	6	4	no	—
234	C₅×D₄	—	12	4	no	—
235	C₅×D₄	—	12	4	no	—
236	C₅×D₄	—	12	4	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	3	1	no	—
239	C₂×C₄×C₅	—	3	4	no	—
240	C₂×C₄×C₅	—	3	2	no	—
241	C₂×C₄×C₅	—	6	4	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	12	4	no	—
244	C₂×C₄×C₅	—	12	4	no	—
245	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
247	C₅×C₈	—	3	4	no	—
248	C₅×C₈	D₃×D₄	1	4	yes	—
249	C₂×#41	—	3	2	no	—
250	C₂×#41	—	3	2	no	—
251	#135	—	6	16	no	—
252	C₂×Q₁₆	—	3	4	no	—
253	C₂×SD₁₆	—	3	4	no	—
254	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	—
255	C₂×D₈	—	3	4	no	—
256	C₂²×C₈	—	3	2	no	—
257	C₄⋊Q₈	—	3	1	no	—
258	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
259	#127	—	3	1	no	—
260	#127	C₂×C₅×D₃	1	1	yes	characteristic
261	#124	—	3	2	no	—
262	#124	—	3	2	no	—
263	#121	—	6	2	no	—
264	#121	—	6	2	no	—
265	C₄×D₄	—	6	2	no	—
266	C₄×D₄	—	6	2	no	—
267	C₂×C₄²	—	3	1	no	—
268	C₄×C₈	—	3	2	no	—
269	C₄×C₈	—	3	1	no	—
270	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
271	C₂×C₃×C₅	—	8	2	no	—
272	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×#135	1	2	yes	—
274	C₅×D₃	—	2	2	no	—
275	C₅×D₃	—	8	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂²×D₃	—	2	2	no	—
278	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
279	C₃×Q₈	—	2	4	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	4	4	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
284	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
285	#67	—	4	4	no	—
286	C₂×Dic₃	—	2	2	no	—
287	C₂×Dic₃	—	4	4	no	—
288	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
289	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
290	D₁₂	—	2	4	no	—
291	D₁₂	—	4	4	no	—
292	D₁₂	—	4	4	no	—
293	C₄×D₃	—	2	4	no	—
294	C₄×D₃	—	4	4	no	—
295	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
296	Dic₆	—	2	4	no	—
297	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
298	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
299	C₂²×C₅	—	3	2	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	4	no	—
302	C₂²×C₅	—	6	2	no	—
303	C₂²×C₅	—	12	2	no	—
304	C₂²×C₅	—	12	4	no	—
305	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
306	C₄×C₅	—	3	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	6	2	no	—
309	C₄×C₅	—	12	2	no	—
310	C₄×C₅	#916	1	4	yes	complemented
311	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
312	#41	—	6	8	no	—
313	#41	—	6	8	no	—
314	C₂×Q₈	—	3	2	no	—
315	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	3	2	no	—
318	C₂×D₄	—	6	2	no	—
319	C₂×D₄	—	6	2	no	—
320	C₂×D₄	—	6	2	no	—
321	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
322	C₂²×C₄	—	3	1	no	—
323	C₂²×C₄	—	3	2	no	—
324	C₂²×C₄	—	6	2	no	—
325	C₂²×C₄	—	6	2	no	—
326	Q₁₆	—	6	8	no	—
327	SD₁₆	—	2	8	no	—
328	SD₁₆	—	6	8	no	—
329	D₈	—	6	8	no	—
330	C₂×C₈	—	3	2	no	—
331	C₂×C₈	—	3	8	no	—
332	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	6	2	no	—
335	C₂²⋊C₄	—	6	4	no	—
336	C₂²⋊C₄	—	6	4	no	—
337	C₄²	—	3	2	no	—
338	C₄²	—	3	1	no	—
339	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
340	C₃×C₅	#3147	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	4	2	no	—
342	C₂²×C₃	—	4	4	no	—
343	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
344	C₂×D₃	—	2	2	no	—
345	C₂×D₃	—	4	2	no	—
346	C₂×D₃	—	4	4	no	—
347	C₂×D₃	C₅×#127	1	2	yes	—
348	C₃×C₄	—	4	2	no	—
349	C₃×C₄	C₅×#135	1	4	yes	complemented
350	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
351	Dic₃	—	2	2	no	—
352	Dic₃	—	4	2	no	—
353	Dic₃	C₅×#127	1	2	yes	—
354	C₂×C₅	—	6	2	no	—
355	C₂×C₅	—	8	2	no	—
356	C₂×C₅	—	24	2	no	—
357	C₂×C₅	D₃×#127	1	1	yes	characteristic
358	C₂×C₅	C₂×#916	1	2	yes	—
359	C₂³	—	2	2	no	—
360	C₂³	—	3	1	no	—
361	C₂³	—	6	2	no	—
362	Q₈	—	2	4	no	—
363	Q₈	—	6	4	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	6	4	no	—
367	D₄	—	12	4	no	—
368	D₄	—	12	4	no	—
369	D₄	—	12	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	3	1	no	—
372	C₂×C₄	—	3	4	no	—
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	6	4	no	—
375	C₂×C₄	—	6	2	no	—
376	C₂×C₄	—	12	4	no	—
377	C₂×C₄	—	12	4	no	—
378	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
379	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
380	C₈	—	3	4	no	—
381	C₈	C₅×D₃×D₄	1	4	yes	—
382	C₂×C₃	—	8	2	no	—
383	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
384	C₂×C₃	C₂×C₅×#135	1	2	yes	—
385	D₃	—	2	2	no	—
386	D₃	—	8	2	no	—
387	C₅	#81760	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	3	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	6	2	no	—
392	C₂²	—	12	2	no	—
393	C₂²	—	12	4	no	—
394	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
395	C₄	—	3	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	6	2	no	—
398	C₄	—	12	2	no	—
399	C₄	C₅×#916	1	4	yes	complemented
400	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
401	C₃	C₅×#3147	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	6	2	no	—
403	C₂	—	8	2	no	—
404	C₂	—	24	2	no	—
405	C₂	C₅×D₃×#127	1	1	yes	characteristic
406	C₂	C₂×C₅×#916	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#492	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#492	D₃
hypocenter	C₃	C₅×#3147
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#492

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#916	C₂	semidirect
2. C₅×#5725	C₂	semidirect
3. C₅×#5716	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₅×#5168	C₂	semidirect
6. C₅×#5092	C₂	semidirect
7. C₅×#5073	C₂	semidirect
8. C₅×#4693	C₂	semidirect
9. C₄×C₅×D₃×C₈	C₂	semidirect
33. #81760	C₅	direct (N × H)
41. C₅×#492	D₃	semidirect
70. C₅×D₃×C₈	D₄	semidirect
71. C₂×#916	C₂×C₅	semidirect
72. #5725	C₂×C₅	semidirect
73. #5716	C₂×C₅	semidirect
74. C₃×#492	C₂×C₅	semidirect
75. #5168	C₂×C₅	semidirect
76. #5092	C₂×C₅	semidirect
77. #5073	C₂×C₅	semidirect
78. #4693	C₂×C₅	semidirect
79. C₄×D₃×C₈	C₂×C₅	semidirect
183. #492	C₅×D₃	semidirect
193. C₃×C₄×C₅	#135	semidirect
225. D₃×C₈	C₅×D₄	semidirect
310. C₄×C₅	#916	semidirect
340. C₃×C₅	#3147	semidirect
349. C₃×C₄	C₅×#135	semidirect
387. C₅	#81760	direct (N × H)
399. C₄	C₅×#916	semidirect
401. C₃	C₅×#3147	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#916	2
C₅×#5725	2
C₅×#5716	2
C₃×C₅×#492	2
C₅×#5168	2
C₅×#5092	2
C₅×#5073	2
C₅×#4693	2
C₄×C₅×D₃×C₈	2
C₅×#3147	3
#81760	5

Subgroups — C5×#81760 #14438880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81760 #14438880