Subgroups — C₅×#70375 #14299864

Order 1920.

524 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5819	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₅×#5236	C₂	1	1	yes	maximal, characteristic
4	C₅×#5125	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4559	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1861	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₅×#948	—	2	2	no	—
13	C₅×#948	—	2	2	no	—
14	C₅×#926	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	—	2	2	no	—
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₂×C₅×#208	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	C₂²	1	1	yes	characteristic
19	C₃×C₅×#104	C₄	1	2	yes	complemented
20	C₃×C₅×#104	C₄	1	2	yes	complemented
21	C₅×#837	—	2	2	no	—
22	C₅×#819	—	2	2	no	—
23	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
24	#70375	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#568	—	3	1	no	—
26	C₅×#430	—	3	1	no	—
27	C₅×#423	—	3	1	no	—
28	C₅×#421	—	3	1	no	—
29	C₂×C₅×#104	D₃	1	1	yes	characteristic
30	C₅×#344	—	3	1	no	—
31	C₅×#339	—	3	1	no	—
32	C₃×C₅×#41	—	2	1	no	—
33	C₃×C₅×#41	—	2	1	no	—
34	C₃×C₅×#41	C₂×C₄	1	2	yes	—
35	C₃×C₅×#41	D₄	1	2	yes	—
36	C₂×C₃×C₅×Q₈	Q₈	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	Q₈	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₃×C₅×M₁₆	—	2	1	no	—
43	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₃×C₄²×C₅	—	2	1	no	—
46	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₅×#217	—	2	1	no	—
49	C₅×C₄⋊Dic₃	—	2	1	no	—
50	C₄×C₅×Dic₃	—	2	1	no	—
51	C₅×#208	—	2	4	no	—
52	C₅×#208	—	2	1	no	—
53	C₅×#208	—	2	1	no	—
54	C₅×#208	—	2	1	no	—
55	C₅×#208	—	2	1	no	—
56	C₅×#208	—	2	1	no	—
57	C₅×#208	D₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	4	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
62	#5819	C₂×C₅	1	1	yes	characteristic
63	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic
64	#5236	C₂×C₅	1	1	yes	characteristic
65	#5125	C₂×C₅	1	1	yes	characteristic, complemented
66	#4924	C₂×C₅	1	1	yes	characteristic, complemented
67	#4559	C₂×C₅	1	1	yes	characteristic, complemented
68	#4523	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
70	C₅×#131	—	6	2	no	—
71	C₅×#131	—	6	2	no	—
72	C₂×C₅×M₁₆	—	3	1	no	—
73	C₂×C₅×M₁₆	—	3	1	no	—
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₅×M₁₆	—	6	2	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₅×#117	—	3	1	no	—
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₅×#108	—	6	2	no	—
80	C₅×C₄⋊C₈	—	6	2	no	—
81	C₅×#104	—	6	2	no	—
82	C₅×#104	Dic₃	1	2	yes	complemented
83	C₅×#104	Dic₃	1	2	yes	complemented
84	#1861	—	3	1	no	Sylow
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂³×C₃×C₅	#41	1	1	yes	characteristic
87	C₃×C₅×Q₈	—	2	1	no	—
88	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	—
89	C₃×C₅×D₄	—	2	2	no	—
90	C₃×C₅×D₄	—	2	2	no	—
91	C₃×C₅×D₄	—	2	1	no	—
92	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	4	2	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₅×Dic₃	—	4	1	no	—
106	C₃×C₅×C₈	—	2	2	no	—
107	C₅×C₃⋊C₈	—	2	2	no	—
108	C₅×C₃⋊C₈	—	2	2	no	—
109	C₅×C₃⋊C₈	—	4	1	no	—
110	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
113	#948	—	2	2	no	—
114	#948	—	2	2	no	—
115	#926	C₂²×C₅	1	1	yes	characteristic
116	C₂×#208	—	2	2	no	—
117	C₂×#208	C₂²×C₅	1	1	yes	characteristic
118	C₂×#208	C₂²×C₅	1	1	yes	characteristic
119	C₂×#208	C₂²×C₅	1	1	yes	characteristic
120	C₃×#104	C₄×C₅	1	2	yes	complemented
121	C₃×#104	C₄×C₅	1	2	yes	complemented
122	#837	—	2	2	no	—
123	#819	—	2	2	no	—
124	C₄⋊(C₃⋊C₈)	—	2	2	no	—
125	C₅×#41	—	2	1	no	—
126	C₅×#41	—	2	1	no	—
127	C₅×#41	D₁₂	1	2	yes	—
128	C₅×#41	C₂×Dic₃	1	2	yes	—
129	C₂×C₅×Q₈	Dic₆	1	1	yes	characteristic
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	Dic₆	1	1	yes	characteristic
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
135	C₅×M₁₆	—	2	1	no	—
136	C₅×M₁₆	—	3	2	no	—
137	C₅×M₁₆	—	6	4	no	—
138	C₅×M₁₆	—	6	1	no	—
139	C₅×M₁₆	—	6	1	no	—
140	C₅×M₁₆	—	6	1	no	—
141	C₅×M₁₆	—	6	1	no	—
142	C₅×M₁₆	—	6	1	no	—
143	C₅×M₁₆	C₂×Dic₃	1	2	yes	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	3	2	no	—
146	C₂×C₅×C₈	—	6	4	no	—
147	C₂×C₅×C₈	—	6	1	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₂²⋊C₄	—	6	1	no	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	—	6	1	no	—
153	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
154	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
155	#568	—	3	1	no	—
156	#430	—	3	1	no	—
157	#423	—	3	1	no	—
158	#421	—	3	1	no	—
159	C₂×#104	C₅×D₃	1	1	yes	characteristic
160	#344	—	3	1	no	—
161	#339	—	3	1	no	—
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	4	1	no	—
164	C₂²×C₃×C₅	—	8	1	no	—
165	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂²×C₃×C₅	#123	1	1	yes	characteristic
168	C₃×C₄×C₅	—	2	2	no	—
169	C₃×C₄×C₅	—	2	2	no	—
170	C₃×C₄×C₅	—	4	1	no	—
171	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
173	C₃×C₄×C₅	#120	1	1	yes	characteristic
174	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
175	C₅×Dic₃	—	8	1	no	—
176	C₃×#41	—	2	1	no	—
177	C₃×#41	—	2	1	no	—
178	C₃×#41	C₂×C₄×C₅	1	2	yes	—
179	C₃×#41	C₅×D₄	1	2	yes	—
180	C₂×C₃×Q₈	C₅×Q₈	1	1	yes	characteristic
181	C₂×C₃×D₄	—	2	1	no	—
182	C₂×C₃×D₄	C₅×Q₈	1	1	yes	characteristic
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₃×M₁₆	—	2	1	no	—
187	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
188	C₂×C₃×C₈	—	2	1	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
191	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
192	#217	—	2	1	no	—
193	C₄⋊Dic₃	—	2	1	no	—
194	C₄×Dic₃	—	2	1	no	—
195	#208	—	2	4	no	—
196	#208	—	2	1	no	—
197	#208	—	2	1	no	—
198	#208	—	2	1	no	—
199	#208	—	2	1	no	—
200	#208	—	2	1	no	—
201	#208	C₅×D₄	1	2	yes	—
202	C₂×C₃⋊C₈	—	2	4	no	—
203	C₂×C₃⋊C₈	—	2	1	no	—
204	C₂×C₃⋊C₈	—	2	1	no	—
205	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
206	C₂³×C₅	—	2	1	no	—
207	C₂³×C₅	#237	1	1	yes	characteristic
208	C₅×Q₈	—	2	1	no	—
209	C₅×Q₈	C₄⋊Dic₃	1	2	yes	—
210	C₅×D₄	—	2	2	no	—
211	C₅×D₄	—	2	2	no	—
212	C₅×D₄	—	2	1	no	—
213	C₅×D₄	C₄⋊Dic₃	1	2	yes	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	12	1	no	—
221	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
223	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	#237	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	—	6	2	no	—
229	C₅×C₈	—	6	2	no	—
230	C₅×C₈	—	12	1	no	—
231	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
232	#131	—	6	2	no	—
233	#131	—	6	2	no	—
234	C₂×M₁₆	—	3	1	no	—
235	C₂×M₁₆	—	3	1	no	—
236	C₂×M₁₆	—	3	1	no	—
237	C₂×M₁₆	—	6	2	no	—
238	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
239	#117	—	3	1	no	—
240	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
241	#108	—	6	2	no	—
242	C₄⋊C₈	—	6	2	no	—
243	#104	—	6	2	no	—
244	#104	C₅×Dic₃	1	2	yes	complemented
245	#104	C₅×Dic₃	1	2	yes	complemented
246	C₂×C₃×C₅	—	2	1	no	—
247	C₂×C₃×C₅	—	2	1	no	—
248	C₂×C₃×C₅	—	2	1	no	—
249	C₂×C₃×C₅	—	4	2	no	—
250	C₂×C₃×C₅	#385	1	1	yes	characteristic
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	C₅×#41	1	1	yes	characteristic
253	C₃×Q₈	—	2	1	no	—
254	C₃×Q₈	C₅×C₄⋊C₄	1	2	yes	—
255	C₃×D₄	—	2	2	no	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	2	1	no	—
258	C₃×D₄	C₅×C₄⋊C₄	1	2	yes	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	4	2	no	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
270	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
271	C₂×Dic₃	—	4	1	no	—
272	C₃×C₈	—	2	2	no	—
273	C₃⋊C₈	—	2	2	no	—
274	C₃⋊C₈	—	2	2	no	—
275	C₃⋊C₈	—	4	1	no	—
276	C₂²×C₅	—	2	2	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	—	8	1	no	—
279	C₂²×C₅	#878	1	1	yes	characteristic
280	C₂²×C₅	#886	1	1	yes	characteristic
281	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	2	2	no	—
284	C₄×C₅	—	4	1	no	—
285	C₄×C₅	—	24	1	no	—
286	C₄×C₅	#878	1	1	yes	characteristic
287	C₄×C₅	#882	1	1	yes	characteristic
288	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
289	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	C₅×D₁₂	1	2	yes	—
293	#41	C₂×C₅×Dic₃	1	2	yes	—
294	C₂×Q₈	C₅×Dic₆	1	1	yes	characteristic
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	C₅×Dic₆	1	1	yes	characteristic
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
300	M₁₆	—	2	1	no	—
301	M₁₆	—	3	2	no	—
302	M₁₆	—	6	4	no	—
303	M₁₆	—	6	1	no	—
304	M₁₆	—	6	1	no	—
305	M₁₆	—	6	1	no	—
306	M₁₆	—	6	1	no	—
307	M₁₆	—	6	1	no	—
308	M₁₆	C₂×C₅×Dic₃	1	2	yes	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	3	2	no	—
311	C₂×C₈	—	6	4	no	—
312	C₂×C₈	—	6	1	no	—
313	C₂×C₈	—	6	1	no	—
314	C₄⋊C₄	—	6	1	no	—
315	C₂²⋊C₄	—	6	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	6	1	no	—
318	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
319	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
320	C₃×C₅	#1861	1	1	yes	characteristic, complemented, Hall
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	4	1	no	—
323	C₂²×C₃	—	8	1	no	—
324	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
326	C₂²×C₃	C₅×#123	1	1	yes	characteristic
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
331	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
332	C₃×C₄	C₅×#120	1	1	yes	characteristic
333	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
334	Dic₃	—	8	1	no	—
335	C₂×C₅	—	2	1	no	—
336	C₂×C₅	—	2	1	no	—
337	C₂×C₅	—	2	1	no	—
338	C₂×C₅	—	4	2	no	—
339	C₂×C₅	#4950	1	1	yes	characteristic
340	C₂³	—	2	1	no	—
341	C₂³	C₅×#237	1	1	yes	characteristic
342	Q₈	—	2	1	no	—
343	Q₈	C₅×C₄⋊Dic₃	1	2	yes	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	1	no	—
347	D₄	C₅×C₄⋊Dic₃	1	2	yes	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	12	1	no	—
355	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
357	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
358	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
359	C₂×C₄	C₅×#237	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	6	2	no	—
363	C₈	—	6	2	no	—
364	C₈	—	12	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	4	2	no	—
369	C₂×C₃	C₅×#385	1	1	yes	characteristic
370	C₅	#70375	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	2	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	8	1	no	—
374	C₂²	C₅×#878	1	1	yes	characteristic
375	C₂²	C₅×#886	1	1	yes	characteristic
376	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	1	no	—
380	C₄	—	24	1	no	—
381	C₄	C₅×#878	1	1	yes	characteristic
382	C₄	C₅×#882	1	1	yes	characteristic
383	C₄	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
384	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
385	C₃	C₅×#1861	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	4	2	no	—
390	C₂	C₅×#4950	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#882
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂×C₃×C₅	#385
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#104	D₃
hypocenter	C₃	C₅×#1861
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#104

Complements

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

N	H ≅ G/N	type
4. C₅×#5125	C₂	semidirect
5. C₅×#4924	C₂	semidirect
6. C₅×#4559	C₂	semidirect
7. C₅×#4523	C₂	semidirect
19. C₃×C₅×#104	C₄	semidirect
20. C₃×C₅×#104	C₄	semidirect
24. #70375	C₅	direct (N × H)
65. #5125	C₂×C₅	semidirect
66. #4924	C₂×C₅	semidirect
67. #4559	C₂×C₅	semidirect
68. #4523	C₂×C₅	semidirect
82. C₅×#104	Dic₃	semidirect
83. C₅×#104	Dic₃	semidirect
120. C₃×#104	C₄×C₅	semidirect
121. C₃×#104	C₄×C₅	semidirect
244. #104	C₅×Dic₃	semidirect
245. #104	C₅×Dic₃	semidirect
320. C₃×C₅	#1861	semidirect
370. C₅	#70375	direct (N × H)
385. C₃	C₅×#1861	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5819	2
C₂×C₃×C₅×#104	2
C₅×#5236	2
C₅×#5125	2
C₅×#4924	2
C₅×#4559	2
C₅×#4523	2
C₅×#1861	3
#70375	5

Subgroups — C5×#70375 #14299864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70375 #14299864